tag:blogger.com,1999:blog-63870996380181279592024-03-13T02:26:30.425-07:00Taking the Fun Out of Puzzles & Gamesjoshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.comBlogger24125tag:blogger.com,1999:blog-6387099638018127959.post-40421854269256823272023-10-03T21:23:00.001-07:002023-12-04T08:09:11.283-08:00Errors in McCoy et al.'s "Embers of Autoregression"<p>The thesis of McCoy et al.'s <i><a href="https://arxiv.org/abs/2309.13638">Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve</a></i> is interesting. However, I spotted a two errors early on which make me question the authors' attention to detail as well as their claims in areas that I am less familiar with.</p><p>First, on page 1, <i>Embers</i> mis-characterizes the central claim of Bubek et al.'s <a href="https://arxiv.org/abs/2303.12712"><i>Sparks of Artificial General Intelligence</i></a> and the reasoning behind it. According to <i>Embers </i>(emphasis added):</p><p></p><blockquote>Virtually any task can be framed in the form of linguistic queries, so LLMs could be applied to virtually any task—from summarizing text to generating computer code. <b>This flexibility is exciting: it led one recent paper to argue that LLMs display “sparks of artificial general intelligence”</b> (Bubeck et al., 2023).</blockquote><p></p><p>But the flexibility of LLMs is not what triggered the "sparks of AGI" paper. If that were the case, the paper could have just as well have been written about GPT-2 or GPT-3.5, which are equally flexible in the sense of being able to perform tasks "framed in the form of linguistic queries". In fact, the paper was about GPT-4 and its impressive performance across a variety of problem domains. As the abstract of <i>Sparks</i> states:</p><p></p><blockquote>Given the breadth and depth of GPT-4's capabilities, we believe that it could reasonably be viewed as an early (yet still incomplete) version of an artificial general intelligence (AGI) system.</blockquote><p></p><p>Then, on page 2, <i>Embers</i> mischaracterizes the term "autoregression" in an ML context (emphasis added):</p><p></p><blockquote>The crucial question to ask, then, is: What problem(s) do LLMs need to solve, and how do these pressures influence them? Here we focus on perhaps the most salient pressure that defines any machine learning system, namely the task that it was trained to perform. For the LLMs that have been the focus of recent attention in AI, <b>this task is autoregression—next-word prediction</b> (Elman, 1991; Bengio, Ducharme, and Vincent, 2000; Radford et al., 2018)—performed over Internet text.</blockquote><p>Recent large language models have indeed been "trained" to predict the next word or token, but that is not what "autoregression" means. Autoregession has to do with generating output based on previous outputs. In statistics, an "<a href="https://www.soa.org/globalassets/assets/library/newsletters/predictive-analytics-and-futurism/2017/june/2017-predictive-analytics-iss15-lai-lu.pdf">autoregressive model describes a system whose status (dependent variable) depends linearly on its own status in the past</a>". In machine learning, "autoregression" refers to a process by which a model generates outputs in a loop, one output at a time, where each additional output is appended to the input and fed back into the process to generate the next output. </p><p> </p>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-47129939881615950462023-03-20T16:58:00.007-07:002023-03-27T07:51:59.960-07:00An undecidable Diophantine equation<p>As shown in Jones (1982), it is <a href="https://en.wikipedia.org/wiki/Undecidable_problem">undecidable</a> whether the equation below has a solution over the positive integers for given positive integers <i>x</i> and <i>v:</i><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgY5gLDV3nUfJ1pBBXpu9nY67H-yMeFXhlkAj3LLm9l40G20QFk_eg96_jjiU_XQwSic-7B1raOIhXNP7xLzLci9af9-5UHgigfTcmEeJH1DjXsqXsHhR43aiDQNIqyF0CXI2SVa2wZpVK8cN_BXdeRnDzZ1KKY1EvBTlwTODXtdn195_nQWS1kuZkK" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgY5gLDV3nUfJ1pBBXpu9nY67H-yMeFXhlkAj3LLm9l40G20QFk_eg96_jjiU_XQwSic-7B1raOIhXNP7xLzLci9af9-5UHgigfTcmEeJH1DjXsqXsHhR43aiDQNIqyF0CXI2SVa2wZpVK8cN_BXdeRnDzZ1KKY1EvBTlwTODXtdn195_nQWS1kuZkK" style="margin-left: 1em; margin-right: 1em;"></a><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh01f7zLKbw2S_Kmxfk2uS06PUlcuesNlcQEXVeMuPxcU7Wlm3hlKIjaTNXqGHHcnYYy_2z6zOOBPh36Jbo-mWXkaj72yFPRod4G57e0YKiQgoidZ4gBudvPFPNCsIG3S1Eii8Pvl4KvuxfH8rdBa0OBH485LizklCch17PKlS_z7yTUEClVnvV0i1W"><img alt="$$\begin{alignat*}{2} & &&(elg^2 + α - (b - xy)q^2)^2\\ &+ &&(q - b^{5^{60}})^2\\ &+ &&(λ + q^4 - 1 - λb^5)^2\\ &+ &&(θ + 2z - b^5)^2\\ &+ &&(l - u - tθ)^2\\ &+ &&(e - y - mθ)^2\\ &+ &&(n - q^{16})^2\\ &+ &&(\\ & && ~~~r\\ & &&~~~- [g + eq^3 + lq^5 + (2(e - zλ)(1 + xb^5 + g)^4 + λb^5 + λb^5q^4)q^4][n^2 - n]\\ & && ~~~- [q^3 - bl + l + θλq^3 + (b^5 - 2)q^5][n^2 - 1]\\ & &&)^2\\ &+ &&(p - 2ws^2r^2n^2)^2\\ &+ &&(p^2k^2 - k^2 + 1 - τ^2)^2\\ &+ &&(4(c - ksn^2)^2 + η - k^2)^2\\ &+ &&(k - r - 1 - hp + h)^2\\ &+ &&(a - (wn^2 + 1)rsn^2)^2\\ &+ &&(c - 2r - 1 - φ)^2\\ &+ &&(d - bw - ca + 2c - 4aγ + 5γ)^2\\ &+ &&(d^2 - (a^2 - 1)c^2 - 1)^2\\ &+ &&(f^2 - (a^2 - 1)i^2c^4 - 1)^2\\ &+ &&((d + of)^2 - ((a + f^2(d^2 - a))^2 - 1)(2r + 1 + jc)^2 - 1)^2\\ &+ &&(v - ((zuy)^2 + u)^2 - y)^2\\ &= &&~0 \end{alignat*}$$" data-original-height="1218" data-original-width="1180" height="484" src="https://blogger.googleusercontent.com/img/a/AVvXsEh01f7zLKbw2S_Kmxfk2uS06PUlcuesNlcQEXVeMuPxcU7Wlm3hlKIjaTNXqGHHcnYYy_2z6zOOBPh36Jbo-mWXkaj72yFPRod4G57e0YKiQgoidZ4gBudvPFPNCsIG3S1Eii8Pvl4KvuxfH8rdBa0OBH485LizklCch17PKlS_z7yTUEClVnvV0i1W=w470-h484" width="470" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgY5gLDV3nUfJ1pBBXpu9nY67H-yMeFXhlkAj3LLm9l40G20QFk_eg96_jjiU_XQwSic-7B1raOIhXNP7xLzLci9af9-5UHgigfTcmEeJH1DjXsqXsHhR43aiDQNIqyF0CXI2SVa2wZpVK8cN_BXdeRnDzZ1KKY1EvBTlwTODXtdn195_nQWS1kuZkK" style="margin-left: 1em; margin-right: 1em;"></a></div></div></div><p>That equation corresponds to the 19-equation system from Jones' Theorem 3 (1982). Jones' system of equations</p><p><i> L</i>₁ = <i>R</i>₁, <i>L</i>₂ = <i>R</i>₂, …, <i>L</i>₁₈ = <i>R</i>₁₈, <i>L</i>ᵥ = <i>R</i>ᵥ</p><p>is equivalent to:</p><p> (<i>L</i>₁ – <i>R</i>₁)² + (<i>L</i>₂ – <i>R</i>₂)² + … + (<i>L</i>₁₈ – <i>R</i>₁₈)² + (<i>L</i>ᵥ – <i>R</i>ᵥ)² = 0</p><p></p><p>The single equation above has a solution just when <i>x</i> is a member of the <i>v</i>th <a href="https://en.wikipedia.org/wiki/Computably_enumerable_set">semidecidable set</a>, with <i>v</i> representing the index of each semidecidable set listed in an order determined by the equation. Some semidecidable sets are not <a href="https://en.wikipedia.org/wiki/Computable_set">decidable</a>. Therefore, an algorithm capable of deciding the solvability of the equation for any given <i>x</i> and <i>v</i> would be able to decide membership in undecidable sets.</p><p>Reference: Jones, James P. (1982). Universal Diophantine Equation. <i>The Journal of Symbolic Logic</i>, 47(3), 549-571. <a href="https://doi.org/10.2307/2273588">https://doi.org/10.2307/2273588</a>.<br /><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgUmXuK8qugiC-9RDUxqlt7V92rd2_ULQ0vwYtLI7Jle8TpH0HxXJvfXbRNS8MetDB-nj-UHerTt6HaPh7ydWoZFKK_haEn7szWX_uFgUP5HRSb-1uvKgBKpSe3Nk5PyMrKYTM9FnUd-VI3Rt8iHaws_pGT_un1k2lSsTizKqaP1BuUQq52qUyqzVoA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1046" data-original-width="990" height="657" src="https://blogger.googleusercontent.com/img/a/AVvXsEgUmXuK8qugiC-9RDUxqlt7V92rd2_ULQ0vwYtLI7Jle8TpH0HxXJvfXbRNS8MetDB-nj-UHerTt6HaPh7ydWoZFKK_haEn7szWX_uFgUP5HRSb-1uvKgBKpSe3Nk5PyMrKYTM9FnUd-VI3Rt8iHaws_pGT_un1k2lSsTizKqaP1BuUQq52qUyqzVoA=w620-h657" width="620" /></a></div><br /><br /><p></p>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-19889714570734700492017-10-19T12:50:00.001-07:002018-02-15T16:51:18.837-08:00The high cost of "safe" estimates<div class="p1">
<h3>
<b>A summary of an idea from Goldratt's </b><span class="s2"><b><a href="http://www.amazon.com/exec/obidos/ASIN/0884271536">Critical Chain</a></b></span></h3>
When talking about task duration estimates, I'll define a <b>"true" estimate</b> as an estimate in which we have 50% confidence, that is, an estimate that has a 50% probability of being greater than or equal to the actual duration. Similarly, a <b>"safe" estimate</b> is an estimate in which we have 90% confidence.</div>
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<span class="s1"><br /></span></div>
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<span class="s1"><b>People want to be seen as reliable</b>, so they tend to give safe estimates. But their <b>stakeholders tend to try to whittle down the estimate</b>, so the person often has to fight for their estimate. Now <b>they might look dumb</b> if they finish much sooner than the estimate for which they just fought so hard. Even if the stakeholder is initially pleased when this happens, the person knows that, in the future, their estimates may be seen as inflated.<span class="Apple-converted-space"> </span></span></div>
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<span class="s1"><br /></span></div>
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<span class="s1">If you were to draw a graph of the likelihood of a task finishing at various points in time, it would commonly look something like this:<span class="Apple-converted-space"> </span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZitTAHCFWtGpJQQfYiLnhCnCkJu2VmrqJkkB31BAfaMcVdUk9UbQxW5Imtpz7uXIHXeiaCPed9hvpFO6KmFQ-U42_GUS1STvl2P99A8MgsiMaGoYZY62PSbNA_aJ59hfBBIfD_NR-e04/s1600/safe-est.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1148" data-original-width="1370" height="536" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZitTAHCFWtGpJQQfYiLnhCnCkJu2VmrqJkkB31BAfaMcVdUk9UbQxW5Imtpz7uXIHXeiaCPed9hvpFO6KmFQ-U42_GUS1STvl2P99A8MgsiMaGoYZY62PSbNA_aJ59hfBBIfD_NR-e04/s640/safe-est.png" width="640" /></a></div>
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<span class="s1">Here, the X axis represents time (say, in weeks), and the area under the curve from <i>x</i></span><span class="s4"><sub>1</sub></span><span class="s1"> to <i>x</i></span><span class="s4"><sub>2</sub></span><span class="s1"> is the probability that the task will take between <i>x</i></span><span class="s4"><sub>1</sub></span><span class="s1"> and <i>x</i></span><span class="s4"><sub>2</sub></span><span class="s1"> weeks to complete. Since there a chance that the task will take a long time, the curve has a long tail on the right-hand side (not shown completely in this graph) that drifts down to 0 very slowly. The area under the entire curve is 1, reflecting an unrealistic assumption that the task will definitely be completed at some point in time.<span class="Apple-converted-space"> </span></span></div>
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<span class="s1"><br /></span>
<span class="s1">The area under the curve from 0 to 1 is about 0.5 (as you can see noting that the green area of the graph is slightly less than a 1 x 0.6 rectangle), so the probability that this task will take less than 1 week is about 50%. In other words, the 50th percentile time for this task is 1 week. The probability that it will take between 1 and 2 weeks is about 25%. The probability that it will take between 2 and 4 weeks is about 15%. And the probability that it will take longer than 4 weeks is about 10%. Adding these numbers up, we see that this task has a 50% chance of finishing in less than a week, a 75% chance of taking less than 2 weeks, and a 90% chance of taking less than 4 weeks.<span class="Apple-converted-space"> </span></span></div>
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<span class="s1">So, an estimate with 90% confidence<span style="background-color: white; color: #959595; font-family: "open sans" , "verdana" , sans-serif; font-size: 14.4px;">—</span>a safe estimate<span style="background-color: white; color: #959595; font-family: "open sans" , "verdana" , sans-serif; font-size: 14.4px;">—</span>will have to be <b>many times longer</b> than a true estimate.<span class="Apple-converted-space"> </span></span><br />
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<span class="s1">For more on this topic, see Cutting Edge's excellent white paper on <a href="https://web.archive.org/web/20070113202349/http://www.cuttingedge.ch/articles/IntroToCriticalChain_Part_ii.pdf"><span class="s3">Managing Duration Uncertainty</span></a>.<span class="Apple-converted-space"> </span></span></div>
Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-69209086257615887342016-01-11T18:39:00.001-08:002016-01-19T17:56:49.463-08:002011 Sprouts Clash of the Titans - Game 2 Analysis<html>
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<h1>Clash of the Titans, Game 2</h1>
<h2>Analysis by Josh Jordan</h2>
<p>For background, see my <a href="http://www.takingthefun.com/2016/01/2011-sprouts-clash-of-titans-game-1.html">analysis of game 1</a>.
<p>22- (Khorkov - Jordan+Aunt Beast*) 1(23)1[2-10] 1(24)23[11-14] 11(25)24 2(26)2 2(27)26[3] 15(28)16 15(29)16[17-19] 15(30)17 16(31)20
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erCM8asKoi98XQpsGOxmTRmjuzL6wyPSzjOm828kR9QZhnFB4sPKLxkSyCyON25RJOGjDhIVknv4WYU34jFltJY+jqmdo0X8onjM5J4xiqMa4PvLqnsFiy2lMbSF79obrbwhuPs7TC6Y9+qzkuAo1icNw2+5evi/WHxf/7/9fP/wyj8qIqaNK6uvIKrs9hMGjNHxrV1sLsC4uc/w5U+gG4wPXwxrFCoTLPUpJZal8Vm0pg5Mquq4x01IB7iuEnr8+3wxeByoT4NEpRd5BNYXHdJR97nGtSxvQsKiylnryl2YIog7WtA1mN2kRVZnF0a2UKBtUaBq1iMg2Pt+j+ANlosPkAa7eqBfcp5ca1SXVT9IXJ8PbEplHJ0hrAqLD5DGqW6gdlagYLjz5p5G/A5MY7giUKNIxolkjOEPY3FZW9TUug1xqynM3PEV3K+nSY/zbUPc0XLT6uBhWMklWexgTRviJnf89aP+AxK5M1F86RRLxIzR1JL2Ot8DepNaoGPnXQByy5f1tpJYgqzWE+aIUnrF4fPgt7468Xlho/Pt7LVWTZ870vDkazNXo3PV5QElF1XYy1jzKqC7Bk/TEZhECipQzG78Vy+xtZeNazOAovnijWJfruceF1KV9M9GU8paUF355k6T8DoLKZ3jtsstrxzBIuXWHweQeoVnUcTs3wdKZ0ki8UFWjW4+h4plzvHBsd65WvmSHYJq0mX9W5s7arFSml7qmhxWbynOPN9FHtOV4usUHJ14up4M0ergeHmvShgU3KCCfI1dbBcYiyW1YhvbdvC9kTfGl31HrlrviQFwPFG0a5OSTQeLB4ky54FN3ik7wp7NeixKY28cMmrSh4vUUQWS4m+bWd74mp5lceGxh5//Np7pIsTOTb6KlZHPncqq7NuGH+JMjK5l60hKWscO5y5q9vDvtQsV7eqRrk+7U3MPit+aowVvkeQcCyWlX7b2vbE1Up9HJm5qzvxcmS8GrPBeGNBDFZEd2F/babHZjnyNh0EWCy7beJYk43krYi9WFzHY7PS1W0cM6rVVWyPx/K3pUs6MRaLNeqPY5Mzl1IQxb62o3kwvt7nVymKjKeOiZkXA7XvXDhYPCst7ZoAiyfqa4tvwBS+i+vu0/9aMF+3jBa4y5YVTtYa/ymQRjylSspxrf25bbMu1WVydkXYwDiL2ph7A5FvWOPH7elGZegdNWrsPY5NztwlYc0cDa8ES6FaDraXxXJ1q75OpdWp61rO7+oEPRD/WNbYe0OblFZ0OKZuZgU7XI2FczIbZy6UaXJxErlOWgt/y7DOKGT3iay1yTWjORwYijgcQ7m111sFP9kZLUDPSX1mTGg5OURm26ssJ52yaspae2NxA9nhlZky5q2L11sFJ1N550LPSe4y9pUZY7bZPtf1xRTOUsYMWQxwiFctJP2UlHLg9mlEe0CKILVFmNsHi/8skuGR3OdRxnCibzrP8w4W03MakHcBQ6LraTxyn8Xim0TcYJGyP+etOUs/L56cQb8dWRin80h3eoVxpFxPKQpCcPV3gst6PzVH/bpuZHFdrJ+HcUMQ0F+8p5L0VgoWc7RlkpH4t3KYXjgLPGZuIBYrtZacnUxnLsfLMcWktBBoKyXs8EHI8+LQxeffVhfsvqXWmNcOWDzLHf1EGLzQ2wPQVk/b+hyvJzXz7/kahH2SixtZTL+fmh801z8FL/R2BbTV03ZuGSy2VH6TxUrbQ8Nsz9P5Izj6Ty3zdLMvjaq4Wc+ltRPPi5dsYvBQgetY3Kgw3+egQJBtg0Q4JmL1fRSOoaZ2HYvF4o/vPvcwWJyifD/zmGIVeYOE/ga5u5TFlOe/qD+D+iO6QC6IQikNg/5Kwv46Ed3zoZobKeMUO29jKHP3pLOfRbnwiESl5+ikdIhIbWwE+hsIHq4vFjymoBSQC4v1mNVXTP2mEYog2zWn6kg18u0lnzGxf7jd1yf0N8h1RBaL4JhYPcNhxLl76VFlVv9ksnGntLTei6wjWWt7iTty1pO4srSey28/OlIN30WdxuLyzJfY8BqzWJtZYLHvdsrl/Sn+CYt/nWbe+mfozHIalMV7rTHxvZA1EIc39Xrqg8V72qIv3tONMgsspqhkMCYui1dxLPIZIe09b8ziR8P5tUeqyFQdaedFSoSMdnoWl1SiL7ZMaGgWF5RQFOGz2GbDqzJrKNRwa1EkXR2j58gmNavrPWN8w+K3Nhkp0E53dBY/66fUAZPFFBdSydBjllSE0exYZifa2rXjmZxRNLIjC6q5yMHi5l67KNLcfTc4JpbOY0RVZRhnKoAEMQWcTAeL9bRdsrzJIN+9Mekrm8/Ovx2V2hyhLmXCcnBzTqKaTRGpVSO0VD6gL7A4SFJSsnhPOxEo7LmmzPIKTxVzUje5qkFSsnPwmD5Hb70OsqBaBhexWFVHpnEpZm2EobrBRNalGuGGYtdOQSJUU7/J4ucAVzWyq4x7iantFyw+qYy1q+UkrTbWss/TIIkZ3tp73e9vJOCZ4iWmgV9+LgyC3E7cbRORC72M52bxsO0S6cX0FB9afmJ+O6dTCsZgX4nkwiBOJYXPM4tc6OU0N4sbXQrR9PRSsvxQuBi3qXgDL2CxUsF4mTWoGa+lufsFi91TMDijMKh4Axf92cue071ZIfJ6XBDIhV5K91nseMr5JkfdFxvf7zMzJNI/LsVgs6n467KJc0m6mwcjHXrZP4fFpUpc7veZGeIzazUAs01VLop7HvdmraqB8XQFkBG6VksjD2Hx5LA1S+kwmbWU9USDs6QvkaTMUJERpoCvt/Ucu0GyMm8qgwTJ0fnmuUhftOwjI0oZSd8X95Vhf7+vlBuYDfhMAkkBi5VqgMVi961S39fXx8S431cqF2Oz2PbGglPcISkUlTbG5GbxxoIxJZEC2PYxk4W8aOSFy2L31lhDFNiMoAA2fIQsDGNAajRSAxZrqAqbAgpgwwuIqGMCqdHQFSzWUBU2BRTAhhcQUccEUqOhqwCLcUyhkZjLbWK3Ry4AZEcjO2CxhqqwyVUAu52roPJ8JEhcYBkWozUWT8zNBrHP42cfORLPEVgsLikMchXAPucqqD8fORLXGCwWlxQGuQqk3uf954+WXuFqZzU/dY6sRFrzI8ZiHFOsCY/RLwpk3+Sc+Dlz+QU1+bTq8DcN1J905XuHBbAYNRBLAV8e8bXgxM+Zy4y8cV1/2zO36fSZrjH9UUCSxWiNUVVMBRxhxIy8TF9dQkM9qTCYdkpUz396NAPHTIX76WCxuKQwuK/AKsj2PanNXFpC03IuzVVbwV89WvXXF8FiVan/uYrLuolTTLLrymut9C8plnBA/SwtIRqL36oFfbHB9hHui3FMQc+ZASVz3UguUYyus/FI+iqGt//G0b65m/TFzx6vv4LEnD0MeRYDx5SaMKjmxkXTglGCtBxDR5hlVBu+6AvJy+IaxxsSYcpQgRtZPITU6oucerKhpI0Xjg71XDrCpDwq2ek7yuENUBnW3P4rRbVqdt4X/3PE+ftYedULxv/aAkpyRN5a/NiYFmwoaeNFpH6YeorEIGVkwtbhj4Kw+PNQYtzKgcVSdSP+nrYUnQ5/5zMtmFHS4CSEX4pMMfkByFqgsLgvgCcGXynqqBpN3gLzDVg2ce7WVM4ogt/CLBXQcPCShbeGYlL6gmUxvEEWtM80xVeSGYD4dAqL31qWdGqkC1g83YIGweKZmA/I+hEiJRickoJFNjEloqRNqEQvYDFRKAxrbz60FQm42YghPcP0WKyt/Nx+sy6bJp145+urDNP7KovfemRmGGbTibvJLJ68jnT74keXaNlaiseYxTZMbPr9nssGBb2UBYN4pFyAxVJK3mYHLP7IuCWLbZjY9/s2fm9oipvOY1XYjNenjDHHpLwFi6O1xkvVcx6L+5uVVWTwS3kpBXx3lhbQF1uqfZIvIxaHwvESCMBi8XJf0l/cu7ZBzkF8RmUyxqxdA3v2weJ/dKNjV6n+mpZKyYt7X6y6rr1tIDiLszrOXMElrJpKGvbqMrXH27E4Tmv8xlx3Fj8SPV/acnFupTlFefy+5SyQM5eTFObcpGEzVy0+3ZTF2nwhqtOXzoR9dEATvdOHqZa4C4tVV0QXVnUkZ42cuaqLmhtPGrajYkPX1iyOgOO30qGXFH0kJ9+qXuxZrLocjs6yc8udzd5/ZIOxsXZJZrXFdGCxO47DsnjCR/E6aESowSHuyz3jGiuCzaIAWCxSDD4s9t2cYVn8yPJ8iWQ3iJHDlhNE1VBhIMX8dHjuea/8RWYxP6PRLHhlOZoOZ8eDLPPz68lir+4YLObXDdECtihRqOzD6Ik+8s5PJH3OLHbBMVgsUjqfRuj789MUBgRXgJjr5nkmc1GHYd2fxfY4BouZe4Aynbg5KaYwJr4ClHQ3IGY+F5HFegSFQ7C4PLOyUYRSN/NI+BZsVurihbnHXGKGU74Cn5tCkMWCpvgLl7IQhcXPej7TKbJsvhe+BZGFBDQCZQImxSakz9QLAlTQlI04FC+xWGyD42EiV1+kiHvbmM/deJsgV62Xkn2pgwWw2Ki0KEk1CgVuyAoga2SpzhxILACpB25SWI+TjHB9cTmsIKY2jpTXRoID4mtTXy/cfsNKYT1I+oKy2PL4OEgmkoZhvwOTCnVD2CgGTpZDs/g5PkaCOQnWm4vU6Gmb1DK2Kidx0VmMBpmTXb252HV62ua1/FkV9SFvs8zPuW+yDG1OHIWVNweL0SDHKSC0w3FyES2SOU+bn9bfbhfV0ObEUTTFfh24Rw6uj2374plrmWGjhf5hUxMhsKXyKIOf/yzNnfTIeaGRpi8uEm9fQiMUa94YIHve3FlGTkeqRvc69E4PyVKowTXD1/229yz6bi8w1ESoHSodkYOhlwpY3J6YR87rPDZ0aga5g8gGIp/kgsjifhhx4kSr1E3xn6c02esAsFDKIIRVEvZssxSkakBTw6ZxptKz+NEL4BCsG4gpKOZtpj5Z/Dbgc+LBHfHfEDupVgARZjYhIFNATH8aozcd9n70eVbZD+CQ3SuJh/TFtXwPUDImw60IoJiX9Cf6nXS+ZW/2O3RvwzYGHyPDF+MrfSCLi+gg8mf9QaJPiTBgVYE9qq56OW/8ySzGUfL8iA175rz9HGFFqKu9LJzP4prIqBIc4OztE8yiK4BdRtfq1+Hq3rS8s669K7924XlrNWnkYPFe4m7pixt16tP9PeFSzLpkmSlycVWQwPFGui9l8a9bg4pYGwpGmwL+RsvIhfGAxRtJB4t/iZYUZEnD3qhXTEmhAFi8kSaw+FW04IALHt5GLWLKMQqAxRupBItJorm/e9w9AJJMGAQF/lIALN4oBLB4Q7S/q63nY/MK0fSnHVQ2UUkMi6MAinY1F2DxqmIL4ymQRckuCIqheRRAYa/mCixeVQzjoQAU+FYALP7W6PcIsHhVMYyHAlDgWwGw+FsjsHhVI4yHAlBgVQG8z2dZsdUJGA8FoAAU+FRg7zn2p9mDB+CM4uDkYmlQwEeB4VNrn1DyeAWL8+QKkUKBJAqAxRuJAos3RMMUKAAFZgqAxRv1ARZviIYpUAAKfCiA8+LVEgGLVxXDeCgABUgKFByTRl8/CCy+vgQgABSAAgEUAIsDJAEhQAEocL0CYPH1JQABoAAUCKAAWBwgCQgBCkCB6xUAi68vAQgABZQVGH4eGh+SblQHi5XLEOahwN0KNL8k6Pl2+OLdOv0BFl9eAFg+FDBVACx+kxssNi1EOIMClysAFoPFl28BLB8KhFAALAaLQxQigoACNytQjolxXtyXAc4obt4aWDsUsFOg5i9YDBbbVR48QQEoUBSYwxd/kOnP95agXKAAFIACqgr0qEVfjL5YteRgHApAgVaB/ncZPyPwWY9GKfTF2DxQAApAAX8FwGL/HCACKAAFoABYjBqAAlAACvgrABb75wARQAEoAAXAYtQAFIACUMBfAbDYPweIAApAASgAFqMGoAAUgAL+CoDF/jlABFAACkABsBg1AAWgABTwVwAs9s8BIoACUAAKgMWoASgABaCAvwJgsX8OEAEUgAJQACxGDUABKAAF/BUAi/1zgAigABSAAmAxagAKQAEo4K/A/wDyVWDElmOTsgAAAABJRU5ErkJggg==" width="473" height="279">
11(32)11[12]
<p>Aunt Beast doesn't know who wins this position, but she can see that Roman loses if he moves in the 0<sup>4</sup> component.
<hr><img class="pos" 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" width="473" height="279">
20(33)31[21,22] N
<p>Roman moves in the 0<sup>4</sup> component, changing it to a 1<sup>5</sup>. In a way, Roman's hand is forced: he wants S(17) to have the nim-values 1<sup><i><font size="+1">x</font></i></sup>, and this is the only move that does that.
<hr><img class="pos" src="data:image/png;base64,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" 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29(34)30[28] P
<p>Move 34 and every subsequent even-numbered move is P. Based on its nim-values, this seems to be another one of those moves which magically win, seemingly at random. As John Conway wrote in <a href="http://www.amazon.com/dp/156881142X">Winning Ways</a>, "You mustn't expect any magic formula for dealing with such positions."
<p>Situations like this demonstrate just how inadequate nim values can be in the analysis of misère sprouts. Understanding these positions will require a fundamental breakthrough in the mathematical theory of misère sprouts games.
<hr>17(35)17[18,19] 21(36)22 18(37)19 18(38)19 19(39@35)38 20(40)36
<p>After move 40, S(3) still has nim-values 1<sup>1</sup> (the sphere hasn't changed since move 27), but S(40) has evolved into a component with nim-values 5<sup>5</sup> — and the result is still a misère P-position! We've truly crossed over into the <a href="http://www.youtube.com/watch?v=NzlG28B-R8Y">Twilight Zone</a>.
<hr>18(41)37[39] 4(42)4[5-8] 4(43)42[5] 3(44)3 3(45)27 9(46)9 9(47@10)46 21(48)22 21(49@33)48 40(50)49[22] II
<p>After a long endgame, Roman concedes.
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</html>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-45403743366396904342016-01-11T18:36:00.003-08:002016-01-11T18:36:58.742-08:002011 Sprouts Clash of the Titans - Game 1 Analysis<html>
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<title>Clash of the Titans, Game 1: Analysis by Josh Jordan</title>
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<h1>Clash of the Titans, Game 1</h1>
<h2>Analysis by Josh Jordan</h2>
<p>Game 1 of the <a href="http://www.wgosa.org">World Game of Sprouts Association</a>-sponsored <a href="http://www.wgosa.org/clash2011.htm">“2011 Clash of the Titans”</a> match between WGOSA World Champion <a href="http://www.wgosa.org/champions.htm">Roman Khorkov</a> and me took place over email in early February, 2011. I was assisted by my computer program <a href="http://www.wgosa.org/AuntBeast.htm">Aunt Beast</a>, while Roman used only his brain. After I won the game, Roman wrote:<blockquote>“This was an amazing game. Very intriguing... It added my white hair. It will be good if you make a detailed analysis. We simply have to bring it to the public!”</blockquote>
<p>As requested, here is my analysis. First, though, let's have a look at these two titans.
<table border=0>
<tr><td><img alt="Roman Khorkov posing on a boat" 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" width="266" height="340">
<td><img alt="Josh Jordan, leaning against a bridge in Paris" 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" width="269" height="344">
<tr><td align="center"><b>Roman Khorkov</b>
<td align="center"><b>Josh Jordan</b>
</table>
<img title="27" class="pos" 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" width="399" height="218">
<p class="left">27- (Khorkov*)
<p><a href="http://en.wikipedia.org/wiki/Sprouts_(game)">Sprouts</a> is a two-player pencil-and-paper game invented in the 1960s by mathematicians John Conway and Michael Patterson. The game starts with a field of dots on an otherwise-empty piece of paper. The move is to add a new dot along with two lines joining it to existing dots subject to the conditions that (a) lines may not cross and (b) no dot may have more than 3 lines coming out of it. (Mathematically speaking, each move extends a plane multigraph of maximum degree 3 by adding a new vertex of degree 2.) The players alternate turns until it is no longer possible to move, at which point the game is over. Like any <a href="http://en.wikipedia.org/wiki/Impartial_game">impartial combinatorial game</a>, <a href="http://en.wikipedia.org/wiki/Sprouts_game">sprouts</a> can be played with two different win conditions: (a) last player wins or (b) last player loses. The former is known as <b>normal</b> play, the latter as <b>misère</b> (pronounced something like "MEE-zair") play.
<p>The top human players <a href="http://www.wgosa.org/gameswithglop.htm">seem to be able to play normal sprouts quite accurately</a>. For this reason, the emphasis in modern tournament sprouts has shifted to misère play. (According to the <a href="http://en.wikipedia.org/wiki/Mis%C3%A8re#Mis.C3.A8re_game">Wikipedia entry on misère games</a>, "Perhaps the only misère combinatorial game played competitively in an organized forum is Sprouts.") However, skill in normal play does not go to waste: the main principle of human misère sprouts strategy is to to create a large component with firm nim-values (see below), in the presence of which the game's misère outcome is usually the same as its normal outcome. (A <b>component</b> is a minimal contiguous region of the game with the property that a move in that region does not affect the moves available in the rest of the game.)
<p>In sprouts, one player <b>serves</b>, that is, determines the number of initial spots and the win condition (normal or misère), and the other player then decides who plays first.. The player who plays first is known as Left; the other is known as Right. Here Roman has served 27 spots, misère. Had he intended normal play, the serve would have been written as "27+".
<hr><img title="Z25" class="pos" 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width="399" height="218">
<p class="right">27- (Jordan+Aunt Beast - Khorkov*) 1(28)2
<p>The shape that results from connects two initial spots like this is known as an <b>anago</b>.
<p>Even though 27- is thought to be a win for Right, I opt to move first, in part to show how a computer can help win a theoretically losing position. <a href="http://groups.google.com/group/sprouts-theory/browse_thread/thread/72ee6decd0525ea6">We're a long way from knowing for sure whether 27- is a win for Left or a win for Right</a>, so in the opening phase I merely try to make the position more complex, in accordance with the <a href="http://books.google.com/books?id=DequBCzoFdoC&lpg=PA18&ots=c8f6kuQcCi&dq=%22enough%20rope%20principle%22&pg=PA18#v=onepage&q=%22enough%20rope%20principle%22&f=false">Enough Rope Principle</a>.
<p>The diagrams here follow <a href="http://books.google.com/books?id=_1pl8so-qsIC&lpg=PP1&dq=editions%3A__3JqZOEp5EC&pg=PA2#v=onepage&q=red&f=false">Winning Ways</a> by coloring Left's move <font color="blue">bLue</font> and Right's move <font color="red">Red</font>.
<hr><img title="24Pt2" class="pos" src="data:image/png;base64,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" width="399" height="218">
<p class="left">1(29)1[2,3]
<p>Roman responds with the analogue of the correct reply in 15-. According to theory, adding a multiple of 6 spots to a region with a large number of spots doesn't change the outcome of the game, so this move should also work for 27-.
<hr><img title="24T + *3" class="pos" src="data:image/png;base64,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width="446" height="227">
<p class="right">4(30)29
<p>Continuing the standard opening for 15-, I make a <span class="desc">*3</span> component in S(2). (The notation S(<i>x</i>) means the entire component containing spot <i>x</i>.) I will try to make more of these *2 and *3 components as the game continues. An identical pair of <a href="http://en.wikipedia.org/wiki/Nim">nim</a>-heaps of size at least 2 make a component with firm nim-values 0<sup>0</sup>. In misère play, when the position contains a component with firm nim-values, further identical pairs of these nim-heaps can can <b>usually</b> be ignored as in normal play, but not always…
<p>It may be useful to recall some definitions and notation. A nim-heap of size <i>x</i> is denoted by <i>*a</i>. The <b>nim-value</b> of a position <i>x</i> is the size of the nim-heap that must be adjoined to <i>x</i> to result in a <b>P-position</b>, that is, a loss for the player to move. A position that is a win for the player to move is known as an <b>N-position</b>.
<p>The <b>nim-values</b> of a position are its normal nim-value <i>a</i> and its misère nim-value <i>b</i>, written <i>a<sup>b</sup></i>. A <b>component with firm nim-values</b> is a component with identical normal and misère nim-values. This is not the same as a <b>firm component</b>, which is a <b>tame</b> component with firm nim-values. A component <i>x</i> is <b>tame</b> whenever there exist nim-heaps <i>a</i>, <i>b</i>, …, <i>c</i> such that, for any impartial combinatorial game <i>y</i>, <i>a</i>+<i>b</i>+…+<i>c</i>+<i>y</i> has the same misère outcome as <i>x</i>+<i>y</i>. (Note that <i>y</i> doesn't necessarily have to follow the rules of sprouts or nim.) Most components with firm nim-values are not tame. A partially-correct table of nim-values for various common sprouts components can be found at <a
href="http://www.wgosa.org/SproutsMisereGrundy2007-4.htm">Playing Sprouts with
Misère Grundy Numbers</a> (Peltier, 2008).
<hr><img title="16Pp7 + *3" class="pos" 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" width="608" height="302">
<p class="left">4(31)4[5-20]
<p>Roman makes a group of 16 spots and a group of 7. If spots 30 and 31 were removed, both of these groups would be components with firm nim-values of 1<sup>1</sup>.
<hr><img title="11(L4)(Pp7) + *3" class="pos" src="data:image/png;base64,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" width="602" height="295">
<p class="right">5(32)5[6-9]
<p>With Aunt Beast, I try to disrupt the human strategy by steering the game into positions in which the normal outcome differs from the misère outcome, even in the presence of components with firm nim-values. Playing those types of positions correctly seems to be very difficult for today's human sprouts players.
<p>I have noticed that many of these tricky positions contain groups of four spots, so I try to create such a group here. This was almost certainly a mistake, since it allows Roman to effectively remove those four spots from the game on his next move.
<hr><img title="11Pp7 + *3" class="pos" 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" width="602" height="295">
<p class="left">5(33)32[6]
<p>Roman simplifies. S(6) is now effectively dead (equivalent to *0).
<p>Dead spots and components which I know to be effectively dead (equivalent to *0, either by themselves or in combination with other components) are colored <font color="gray">gray</font> in the diagrams. Further play in these dead components is pointless.
<hr><img title="Z9Pp7 + *3" class="pos" src="data:image/png;base64,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" width="610" height="297">
<p class="right">10(34)11
<p>Trying again to add complexity, I fall back on the usual approach of playing an anago.
<hr><img title="Z9#3^0 + 5P2#0^0 + *3" class="pos" 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" width="610" height="297">
<p class="left">30(35)31[21,22]
<p>I expect Roman to close off the anago with 10(35)10[11] or 10(35)10[11,12], but he surprises me by playing this move instead, splitting the rest of the position into two components with nim-values 3<sup>0</sup> and 0<sup>0</sup>.
<p>I think it's bad practice for a human player in a theoretically winning position to leave an anago exposed like this, since the opponent can use it to create complex positions that could otherwise be prevented from arising.
<p>In the diagram, the nim-values <i>a</i><sup><i>b</i></sup> of various components have been noted in boxes. When a box contains *<i>n</i>, the component is equivalent to a nim-heap of size <i>n</i>.
<hr><img title="Z9#3^0 + Z3P2:5^1 + *3" class="pos" src="data:image/png;base64,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" width="586" height="302">
<p class="right">23(36)24
<p>Trying to make things even more complex, I play a third anago.
<hr><img title="Z9#3^0 + Z3#3^0 + *2 + *2" class="pos" 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" width="586" height="302">
<p class="left">21(37)35
<p>Roman is now facing two exposed anagos, a situation in which he does not usually find himself.
<hr><img title="9Pt#0^1 + Z3#3^0 + *2 + *2" class="pos" 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" width="585" height="296">
<p class="right">10(38)10[11]
<p>This move looks to have been a mistake on my part. Even if the 0<sup>1</sup> component were equivalent to *0, the remaining components do not make a misère P-position. If instead the 3<sup>0</sup> component is replaced by *3, the resulting position is also not a misère P-position.
<p>My move does have a possible virtue: there are only three replies that make the normal-play nim-values sum to *0 by changing the 3<sup>0</sup> component into a 0<sup>1</sup>, namely 23(39)23, 25(39)36, and 23(39)27. Each of these are subtly different from a misère perspective, and each yields a different unusual configuration in S(23). These unusual configurations are unlikely to have been well-studied by human sprouts theorists.
<p>Instead, though, I should have played 12(38)34 or 12(38)13, both of which better accord with the Enough Rope Principle.
<hr><img title="7(Pt)(L1)#3^4 + Z3#3^0 + *2 + *2" class="pos" 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" width="585" height="296">
<p class="left">12(39)12[13]
<p>Roman returns to a position in which the normal-play nim-values sum to *0. Interestingly, though, he does so by <b>raising</b> the nim-values of S(11) from 0<sup>1</sup> to 3<sup>4</sup>.
<hr><img title="7(Pt)(L1)#3^4 + 2tP1#5^1 + *2 + *2" class="pos" src="data:image/png;base64,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" width="596" height="309">
<p class="right">23(40)23[25]
<p>I have set a trap. Aunt Beast still can't figure out who wins here, but she can see that Roman loses if he moves in the 5<sup>1</sup> component. It's likely that he will, since human players can't abide positions with normal-play nim-values greater than 3.
<p><b>Update (March 2011):</b> In subsequent analysis, Aunt Beast determined that this move is not just a trap — it actually wins! How strange that *2 + *2 + 5<sup>1</sup> + 3<sup>4</sup> would yield a misere P-position. If God doesn't play dice with the universe, he must not play sprouts either, because both seem equally random.
<hr><img title="7(Pt)(L1)#3^4 + *3 + *2 + *2" class="pos" src="data:image/png;base64,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" width="596" height="309">
<p class="left">26(41)26 N
<p>Roman moves in the 5<sup>1</sup> component, reducing it to <span class="desc">*3</span>. Now Aunt Beast can see that Roman has lost. Adopting a notation from combinatorial game theory, I have appended "N" to losing moves, which stands for "next player wins".
<hr><img title="Z5(Pt)(L1) + *3 + *2 + *2" class="pos" src="data:image/png;base64,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" width="577" height="306">
<p class="right">14(42)15 P
<p>There are six winning options here: 34(42)38, 12(42)13, 14(42)14[15-16,38], 14(42)14[15-18], 14(42)14[15-17], and 14(42)15. I like to play an anago whenever possible. Aunt Beast didn't compute the exact normal-play nim-value of the anago component during the game, but in the course of writing this article, I used <a href="http://sprouts.tuxfamily.org/wiki/doku.php?id=home">Glop</a> to determine that it is at least 5.
<p>Adopting another notation from combinatorial game theory, I have appended "P" to winning moves, which stands for "previous player wins". In this case, the previous player is the person who just played the move, that is, me.
<hr><img title="(tP5)(Pt)(L1)#3^3 + *3 + *2 + *2" class="pos" src="data:image/png;base64,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" width="577" height="306">
<p class="left">14(43)14[16-20] N
<p>Looping on a tail of the anago, Roman encloses a group of 5 spots.
<p>According to the "component with firm nim-values" heuristic, this position's nim-values 3<sup>3</sup> + *3 + *3 + *3 would seem to yield a clear 0<sup>0</sup>, that is, a P-position in normal and misère play. Actually, though, it's a misère N-position — a perfect example of a case in which the heuristic goes horribly wrong.
<p>Even though it loses, this is still an excellent move: it leaves me with only one winning reply, a reply which would be impossible to find today (early 2011) without the aid of a computer.
<hr><img title="(tPL4)(Pt)(L1)4^0 + *3 + *2 + *2" class="pos" 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" width="579" height="303">
<p class="right">16(44)16[43] P
<p>This was the only winning move. The fact that this position is P cannot be predicted by a theory that looks only at the nim-values of its components.
<hr><img title="(tPL1L2)(Pt)(L1)#3^4 + *3 + *2 + *2" class="pos" 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uKMhkcxNYmrs2hhoN04k11zvDBol/Tk0WtVuOIo2TXdtqv8k8qpFFUlrzhIVNLRdQJOObpBqd7YIPcq2QXHS+4dRq9SlzT2TCW7oNuExLGXL7ucfQCV56/GA++NaImTzcA1CyWVMiVBCGy7kh19vOTGYfS2nDS+kh3dbQyuVZbgBcMtC7BmieQ8YkRX4edEJ0LZ0E2ZB0axcxTTObEJT8SsWDKJKyF1IiVLMSNVjloqqn07bvd+0TDoEzQjpX+3cRl8t6Qpj94d3HnTvCIDZ/XhWWgVy6TiSsieVMlSzMAq8urEu2I/kNgzGQ8qyMP1ZnJRwSnyjIWj0rU8pRtPwalbHV1vEg4VlOw5NCUgdOmI5k1ODonb5nTrPhzNKSKFi8Z2HDxGA42R2zi8vZ8W4jekfI+H5d8TmKTQOkpWDwGemcePJalNnR1jq/BmMi3A8UvjibCWH1Ip2Qs9s3OIFbktI2NzKI1uCDaZmkpWXrR0czvXG7sqo5Rrh82Po72XXKlkzcl+dG+8VSp1a1JQ9d2k0jwxUamktsUJm09lJcuXxjKeskuyfPr78Tz/Vfr1iEx6XTTCrLgl4iNUTDZdvV8aQ3GS3WhRDh6r+kpmfZRbcKfok/R2xIs7+rWNXdFKJeORnKtiMuCwv5DEg8BAoB5nE0vJ6rHgOCrZgHk1oIab/ALi+nmquO1+cfQaSQXjae9Dr2dGGYvHwN5O2Budx9hZqxgMW81kzTF6Fo8MtJ53NKNfpc/oHgZRkiXXfEgmISHXbnz18dzmXy404ywyV7KNbefTCp7NXWJZ/Cp9Rvf4MFzfiuqI8QE78/PBcG67zy3QB4uo8j7kpGS1nt1xAJX5wK3zGt7ev0pfguTEopyIWVKjXDtiwG4z2nnOas4ZoO5uVyW748nR/3YGRgTNug1E7ZsI+/BEzBF4uxiDlvBo+bmYauvUqLt7j5KdOKJtaW6GOFE7oNTCujXl/pvUeJnKYaSH+AxQP1Kl2sdn4HSE1N29U8maEY0K3adUWwTsJzWGhrFH3pjMj2bHXRXx6beMYsFAI1Tvv1oETZ9CBkjnUggle0saKQchX+/ldaOrO0ccqqSPO8EtEfBpkwwkA8mAnAHSuRRLyerkPed9z1jzAktGsa4kI/1E6hjEoYrN8tdxqURJJ8lAMhCTAdK5FFfJGnJH7wOkGqg4IUXEjXU1rBlzJzBI7YKnI7REfh2XMEQuTwaSgeAM4KfTMUo2Ynz5Ar79qRDpFbxgiDfScGYdmgG4+6PfRkrPgJdLkoFkwIcB/HQ6Xsl8CLWL4nZAdwPhjWLHwI/n5jrSVbL/+/tPnHdgU0JOd1731RFXydMJvxg/eEalkm3rATcNqzMsbRHhU6hyxj0qVf5MlKyxLB62VTEDvxioG7s5hsBTKUlNBgoDYM+kku3pGbA8FuB+Qm//FOo57BpZmojZxLKe1SzoSp9UBiZXtI1tT80i7YMwAPZMKpl3vbaMYnWSRr+AGOdxrmHvyWwpY8UAbHocalpSGXhKMCpEFojKZ9qDPZNK5tcq2zXsSXWjki1HsffjIS5jOZz5tfI4UlfJ8hE4QmnOxYCIWSqZU32RYvhA2aJkVA0rskRVstQzny7qRilNnjPZxircFxo5PFPJzOseZBSbPDBaUwA+J75Fi72w6Jl1aum/ZiCVLPvBgoFUMgtWCT4DalhBP//eRaR1QCIkaiRZm2IGFkjLrDwhTt4SFftKC3b6ic8A0jY5k1nVEWHfKjbmd/IEpAVeKEWj5eWsRN4etXLBSE2rvxgYDWdZi+wPBgNI26SSMYhdLIk8ihXok+bQwi+UsefnoLtPjvX1P8VMv4Mxj+DsVRcLc5xWyUDLwFLMUsk0m0ZLAzQxDXxNBrL6Ts1GIpexrpK9n7DAQMudwM70mwubQnyThMzajYHl/k0l06kFVcMm91kdQCsvpkoGqstynHr7YSvZo4srVvLfIQa6VYBWplEywGJguXlzb7N4/b1oyXITI8J9tou5fJGa0TvBpUohBlQle5+wdRRhUgqNcoWLroxtv5ldQW0mMWRguXlTyUTdQx3Fnoe79x8RCPri+UAmfF2s5afOFJEu5CejG/ZGbrtz4XI/0Lm8cMVSqyY9vFx7IV+ZkgsD882bSsYsAkPDnkhhlUxFXxsZa0Yiqph11eh5J3z+TBxO1jJLfvWyuvpIok23IEua5geXpFkyUE7OCRWpZJw+kVztwypZTQQ7wYmSUWVs9L2LiJ+JyLFT4zRK+DWlGxlIJWtrVWOEziUfZCBnMs2is0exRieoV2DNHMa/4LVE4R33jX7MZyahIM2XL8c1XT6P8yYUId18Q4HRTS29KTKQSqZGJu9874Yf7d6uwqnLnmIitfh1P+Uq4BHpQj4nW/pBFNSCAbU+s3Gk3kXqMOMjVE85HeIMpJLhXA0tVUaxJY6mVM9fu19cupobWJzjb/14SCvCgwjMSMnqM6522JVJJJAFA8Ki2C336V5d/Cdi1mUgvTUMpJKJWmLjjupWTuUIVnHSvJd2fxmHynd8NMr0/LX7RdJHa+okiPrMZvHG7lVJ6HT8KiSkk4eBVDJ+J+w97FLJutPV/IvIQPbo697i8psSW3mTBtyUC1a9tOowkErGaYsImyeVLJWM07ur2yvP5/ZVd988ttMbH0AqGa1GETRsNEprbWYtP4XZ0ST0kPn8KZNQ/Vf8WxAbPwxv7w/haJ1xgrVD99Y1bf7bmiGH7KxTSP9sBlLJCNSpH/GE2JWp3TS2fG5mAB7JWPeTs7e2UX+6GR/UkO9yZOQbc4nuKc+TK94qKp+6mVKjp/1GBibnc/5k9D91ibM9TGVso5J1jzl8Jpt/DySups03oWzcllqhFVu31EgLWz21K+J82jjIvVOdq3Q4YiCVbNEbcbaEtYylkl2mZKTWHQmVnYC9N54uBlL6qRCnM5BKNqxgqJvde2opd8/6n4TtqL75wXmIPZM1/p+/dr+4fE686aMyaus2/NetJewo3vJa0t7YcJ9UHnDPaRmNgVSyfkXUz/Rohe/i0c0alLHmGzSe02cpPMWmPumWPxm9dHvBWEYtYvcaEaRdVbBRCQmSe8IgMZBK1tL15Xuc7p5HBKlRDlDGSD/mLAlB2ksRjBkVVFELo9y1sDFoMcoo3RoxkEr2L7Ff1rCHBd0NT1UyfGAqBxy+5BG/7gA3cqLLhtEGrt3yAGuphUWCith45FgklT4tGEgl+4fVbPRTlIwqSN3XS2T4O6gl2JewJ8eGUouDhu3zjY1dFzZLbPC50I2BVLL8nt1fU6li51nMZN1LOjKZMRayT0xFDhFXPJzNsV74QSI627yxSTSJR5dzyhmOysDXlSzbWv48Neq5jUr2fkW8VckYDSyRAeR8cRNFdiIM0pDE02YjA99VMvY22Fgt69C6O3yXkjVxy18bMVtOcrpsWNSOitCh5xuSLbJufPKSolLnkEiGkDDwUSXD+9jtgimpotZanBYkooWSId+4MVKyeu1Sxh5jJM1dNlR4jf37r/JW7w6+En66OeJfnIemEihJJNdaM/BFJcM72POC2T0F2F/k9Q3ODOJ/rmTs1JaCNFEyRMDqH0pD0txiQ61UV7cK8rnI4QnqKll32JpMYFROfvJiLMHZSEtPBr6lZJNt8CZdd1sui6q4qdiu2Au72S2VjKQr5VsQm//oOqlrx4hSQiyrtsWAWqauUNVfpDocZa27ZahKxlMmrdy3dEIGHd3GamZCP60wSkhtWd1tuQRMhTdxKHElWdu9DUx+WouhMUUdJzKpMpPp8rCsPm5ABTayt1CyR0vqP3hejeUDb6nB3ZajBqVSSvX/2HfPE/YXeRhuXTWv4D1K1r3cLYuaSrakaGmA6w2oah9XMtKZO2/7t5KVhl+WdW6g4oetZEUzSFmQiCV5RoYGqkMHtFRIe+0/oWSSqmtdMJEyS3B277NIUJUr7SQQW8lq5ptfN7V8XWyCTjBM5FOxHLxCCEuzxN8o2VvYtGAz/BQwXVTL1MoMRAoNuiX5rI0V/Su6YqcTauH9SsYuebnPdi+Y9TmrpSJsqMIjTwt/t7N5SjaRovJPuOcPKhnSSxPpQpabHmQqSvYMZzhOkjHuNmcyBlfUJTcrWZEiBikLXn5vj8ndlhRacSNJXEnWksSMJ0WIkjXfqQ++Wwb/Lfh4XUBLXSXr3u0mF775HF8vfHA2XwFzDCVmOObluaHoahnrCINrlYxXaZ74NfdHXmjqlpu3FxuDLozyyDP69sLus+GjQ8t/mgghQ7qaJRICLXY+jodn2azCnXTf8Yr2yN/WukiE8Oz2joVnFQYsejKUzzuVjNro5cbHq43wFCA9PoCXXAYDJBgkokaSU77eXLdTyRp68Wrilu8rC9haSOmjKRn1fkaiESGkq/fIwtHd2gghAimmzYVKtkjpz36tD25hW3gqGXjJlWQkWdvt8qWSvb+Do1lS/7XWP/nsNfkJgSA7llQOkrFdgopKpgWSygzVHsHJ8JlKhhC7vKkQPiwF41mbgTKmfv0EBYbx+DDJiPdPyxIw9hvi860Zb30aqZRQyepyI+JnwcCSopEBDga3ZIMBFwZUsuVhx56DQU6oAIp9t6xxao2nb2q5OPlNY6s7jyBjjH6tp8NGEesj+J3dTUr2/phK63OyyXh300AW52grSBpIERCSMJCMkdOM6rB7IXgCUV0h8I62uUfJlqVtVOH5q6R4o+Vst+DlqyQyAc/GYLdPGkV5fxg2kq7Gsvh5O6R+X8nIXtIVimvxIuKWivC6rmokAZWMqgG6xJK8jS4EdjvUujfs/C+JFR30drjfnpeZPB38/sMGOYmIgFmeAnW/MiSTjcF0nzTaM5eiuljUn4wGRbH74MluCfWFYBFBM3V4y20YU8lIYqbL7dtb3eQNn6lkeMcuy3SGkq3T+Ltf3mKGM/VuskYUa4MlnlFc6kILNY2jZJOnv8nv+Ch1KctrvXz+9Yjf64E3A27JbnhkYfeYVtkXSHSSDYkxkvEcxlza639tjpclt6T07zNe1ugAJZvn8DREs53eXwxS2mU9Rre25e2YmiAVCe6/0RXk+y9GH6G9NanZ/7WYFQ2bKJld1jg/xRIEA5oxAJCWjE7e+uskh9bGOG+45RLz8rDqeuiuUkS1hB3fYMlGdCWbJBBWriZtsa7H+HeL4CIH9uUSDOinq7KToWqpbUWKGk16H6Zd0RopmV2+DKJAMKAZA8AXluDs4ZakmQzcs6lkElaftXGV7D9//nQPSrDz3hfG0dXSZ2MjsMFLLuJK3h88Wmop6srP8otdIUwl45Uj7qqfe1vzP1Ws+B7BLRl7qvQtKTktSKSgMY0RKoIqWZGx5z8Kv6Q5rMn/TQdCkG5pFSPKXck9zKfP5ey1NABnstosBzLdju17eysQQ5BGTlQTwJsct2Q/upBCkIxVOQvnDKEiopI1Mvb8laRh3VKkkoFvHVqNPBKVpYB1v5WjTGn1ZNb9nCz49yv+9RKC/XAIaKZVr5kfqlAt7edaqJcSziFumUqmVx/IE1KaY5QMynhqtBzR5CGWHpCSLJ08BnJXcg9LqEIx6y4vSgYqokOaSx5qAxAPaEYKTTOuxYa28mXduFqOdJjSg6BwJnHLUei5B5J/kjFIxaFmCBX3K1k5+JwnEnAuZPcWUt2lcxUn8ygSMZOsLTPckgRPA5xw3FIZf5EZZb9/3CEytknJ5BfE+XWZVFOSsVGtIrgFeYioZD/0jT4nkzBbMwKyIwmXSlYYYAsSe2FMGcMPyj39+WiM9R9QyVSR4HziluAGLzdpqmeqvXXddvkHebBvXC4Bk+9d5LlMJXvzBnYJj/B61bOfwffAyedkoIcnnBy2ugcEFWKjDMxHwx7QO5TM7Q6hWDtFV8rd4usO5CHibm+IAjNZ0lv8aDlcRuwqR31HE/43A4ARtyASqp7xxG9jfec8gMBAM5Dzd8V/ybynhp2gZLjmgTMZr0xCGOygAReC2+EAJXuKCubTzAHdvzJcBSywFiR/NnB9wi3DPidOGtL6KEQuUlpdRPCzaSbDtUGyIyRr994yCRV0NMX53Klk9URSyGnGlOYgoEraKIRjLaKHwntFMRNkOCvPy8iLIrUxFHPBXSFUIzZ4xO726W4Knk/OKlDJOK4Xa0BuQbPRRUT40LK5Oga0S1zitdimZA3E8lcEeim2hKNcW98etrBR6vjWquZbfia/a/gIDfMZCOZF7J6wW+oOfVRmgAw5W56wuKUBzHT5DwOkKmxTsqZcJCUbDXCkzLNftivZqI7dH43v/mT0QUVEmhOxYaccSMn+1orZ/x4Dgz8gw6CZAcB0+S8DpCqYtAujGg9oEvRulNFoz4D0nSWjbxOdPHTIKzWh1+iXvOwtKMIYYsPO4r012K50Fi5/W5XBd6OADINmOjyklwEDpCpsVrLmnbDZbIolHimcXURF8KauJr/iso5bd5X1g15XyUxJsHYO7knQjIP2z4jT7DiOK8U1yG8QVh3OcIZxS0U+0lVhgMr/ZiVrcDfoqcnI+wAUPLaZHKGuB1wzSi20pud5IhY/Gq9LHckb0smIDSnov8aqYsDEIFmmih/kGTSTpJVrJwxQ+Y+lZE1i1GTidwZbAo0WMpTsIdmhNOo/Gr+xPRC6EBtOCqoywAGgskYvC5Bn0EwluXTyZoDKfyrZp7toqWSjxyhqn32ZZZAr0IzMpJ4GkEP/feX5NRqyfyuxXhY4z7glh5lcM2aAwfw2Jes+JG5/Xfxgd4HveFkadm8g2xKx4QB4CUD9StwM+hz/8zXNt2wI1Ui4vIIKsg2a6fP2eY8M5rcp2fNC9b7yd7/4+craEoC84zko2a39gGxLxIbcBD0Z6wYyif4MZM1MRs7h9wIlMQPzBc2EOeVy+dPiX72WPCYDhYHJ1rVWsotndORARGxojTqYxvyU7AFQYCiJkMrPmYFsg2a0uqT1igEe7alkK16/9O91D82li9dtOJd+By6OiWWJEIXY0IKPZeMdSz/6g/WtZOwPyZrkNUQRzBo0o1UnracM8DhPJcu2+sVAI2bv598/x5Rt56SSifpyu5K9R7EGkkSNJGv/0Aoel6CZqFi5uGKATbjteZQ1Oo4BdiepZDoSTh/5VEnhNT+st5gy59OD3vqV+J/0l4+KQjUSLod/jES5NBYddpdPNuHrbXYXUZnNmgF2M61dwxZ+j2AwJJ4hQiZiQ4i+XcnqV8Tmmz5KGkIpEi5PJSP0k5+pZCOkkvnV6ZRIkn7SytFpdNCCO/aDkInYoEhXR/zko1A0BMluNJytcK6DyDyAnINma7RpATAgYXuhZOW1R+U/gFzSJAQDkpZSScD7wFUB3XOCMInYQACBw92b2Oa78Mu4BuWzMgLyHbkAOQfNVkDz39cMCKleK9kaAmYhBIoFSSsdBvyLNRrC/JHoMPjHC4IfsYFQASe7t5JBuLlGQL6pZFxyvdcJd0EqmXfBToknbCxGmvXc/yx/vwQw3O5dgtCI2KyzEBzra+dhLbhZg5yDZmHpOQWYnOdUslNq7Y1T3lveiEPGQ2hEbNbJcc/0tefIFtysQc5Bs8gMHYFNznMq2RGF3gNS3l57cIeJihCI2EAJcc90yHlYI0HWIPOgWViG4gNTYTiVLH6htyFU6bBt6AMERghEbNapCA70tfPgFtzcQeZBs+AkRYanwnAqWeQS78em0mT709iEAGEPsVnD557ma8/xLbi5g8yDZvF5iolQi95Uspj1jYJKq8+i5OOLA2EPsVmj5p7ma8/xLbi5g8yDZvF5iolQi14FJfuBUv5MyNJCPK9HDeb93zFrGRyVT+GCk8CDh1CH2Cyic49yXlIRV7EYAJkHzSLSEh6TIrcKSlbTNUGmCLopECilP6twy/A94ArQrnauabgHQ3hDbFLJLBgAmQfN3Jvr+IC6xHKUjCdXurifMj7KxCupZC0v4rmr2CSfm7IKcoQ3xMbiHFdJMIoT1iEAMg+aRaHiHBy6xNKUbPlexxM5BvlaOqTlh5HCWUt02+6s3NloEdIQm1QyCwZA5kEzdpN8c6E6qzQlK5NQw35RuElVFKEruhpl9M32mmetTvv1JCOMITYW5/hV5OdMdlQ5FXr+lS9ZyR4QIyjWM5ndCGXn+agem4G16L9ryOkmgjCG2KSSWTAAMg+a3d3JutlZUEpWMva1XY5e7mFZD4cQSwyRDZIfanUQxhCbYVzWOELN4gB7Ig8g56DZAfyEgWhE6RlK5jkwecYK010EIEaNSEBwlClCF2KTSqY7loGcg2ZHteROsHZ8SpWsQWbxumiX/KSkW4LubDE4djIDU/WXIUIXYpNKlkpGaryYxqJWn6YkVbJnr5Y/6tpgl/my0htDL7HtNUhmcP4RrhCbVLJUMrzrYlqK+nyVkoKSrUL88++8NHirQEhzs42hVfCbOklyQHoRohCbo5UMuemCfGrxAHIOmknBf2C9NZOhlcw6+WX/bAewRLjLIJkBmUeIQmy0TvDHj4e0/EFcv9mIMl1dPMGKFAYQe0PASPiLbKyZjKtk1pmDTRIEBojW0yyZQdhGWEJsFJXMSVp+S2YdFOGNbJPfu0imzG+BqMMxmKlkC54caoBVKqJVkrOsCkIRYqOlZI2MPX9dZsE28AtHzALMGjRj8/OFhT4cBlUyn+TBNgoFBsTsZpbkrB691joh4pB+gr/Vxa5bUsnsuD3Cs6i3KRlGVDK35HGiAkLCwVtbJjkHiZmftPwhxeMxky7nyKbIxkZYmth4ErhWsm7r876I8OKZPIKn2IQFRsrCwjiZOUjJfqB6SMtvRkrEhqimc2pgtEZNJaPx5WTteTKsnz6ckq5ucM4RwXCeVQEhxTFLcoQ3UxGBxHO8FrONLfTo1uimSCOEyADoHDTbyGHk0M7spZKhzeBcGBRWGLvkZ1QKkBnQrBOFeI7jossfklZt+SS7RclwnnHLVbqf+3d/6mIpmX/+eIv9588ffMny0am5llI9jx5tqH607COXTytHnh+EGcSmH11JyTSHJIymyErGLweW+8VWW6hLJYM6qsjY8x/QmqlRfdvlFV7uQZ7F2wMvFwskoXwitCA2dkqmPCRh7I+UjHzDo2g5yDNohiX6IatdvKWSrZuskTG5mDUiRN63rw/tGR7WaXMtdrUyF6/HOpAT0KyDmHKUTxJWG5IwUpt86zcGAhWU3HG3uCWW6yesNpKWSrbusK6SddVo7xfXmXhZbGxorxTJcRBOEBu7sezH80ha+MBWLxOjfydENFAyQnRyI1y7YC9pgZRsLxGT/sqZjLr5wpaSmoiiPcIJYuOmZG9VU2TjcTXJl0BFKpl6YVgOCSVj+Z8vulbJ6pcKOW/5ORmVw71tTUXrYA8SApp1AFMOdGQSclayycPmrDqUrHFucUuHzjkixHbG7lSy5pVPpRVG37tYxyqBul9sYDRay/AzUut5dLeecwukUl8HJwghiI3dWDaREz6wMbNvsXxal1ALijHoGTQjgLzdNAJjlKYxrocWHY2MkffGNM35RfX5V8ZltruE4WcZXZeNZUdo1XQZ6AgDhA3E5holU6haKpkCiSIX/I4VhW0XR1Gy0XjBSNZTyd5j1hswo9JdRWRQ0RU2Bh5e6GeVs3ZKoFqvBZkHzTpoKcd6N9nRkMSHZMopJV88BdzSNLn4zkNt7RBK1miPsISpZDWB9bZUFEhqjfJ0KLq+pI7PFeVkX8I4wICSL8gqaHYAOcYQoxG1X8kshEdXGkfCMB+/GFNms6QIj+TuE0TJ3tOh8UYL6h7c/6CZxVgWlLjeZsOhLvksn4IvLZGgjL0/GpElex+ByrNRYYkXerTqTiUrj1rqjE8cjv6JgaHWsFI5tp9mGmD40eq5jaG1UhD6wRnALVtIlElFmM625ZQcl0zqfmey1jVay496jZZ8qkdEHF6rZPM7TjOp1E0zZ40hV4zCFyXDx8H5gFiPRAw8SCeBNnujgyBNzUAGQLOPjmV6Sqb706KN/LAnKi0/6p3Mb0t1KL8d7leyen5iFx5hqalB+SteG4aM1RKCgKznpxFgxM97bZwrHk44kumJNiADoNnnxExPxn6oO+U3+PCbQW+HRMAwyiaEktVipkf7wpOWkr2ry1Cg7hKGn1oIhyWnHARG5Yi8JYxSZozXfJYClNiQRkp2Sw5zJgMrtWQS9GNkFkXJkCNYl4LuC948RFe0urNO/UUQdneJ0E93xg3SkUFggNVRNwPTB80+NJapytjDW35Otmxvfh8uXSsZpJL9UiKqkilV4aNu4m8Pu8KAuYNmfZyUQ98uU03PxIxw9nT/3wfLmSLMvevn/VTDuO+SgOE0ktzqGnsrWU3KaArRzbDrrcDAX/COKKcDdbohvswqmDtodr+YmcnYhOHRP/GKsjz9lpvr/crCQ7IMVAys/eNIFmOGliPET12GkYQ4EMdo3J/sHIAhHN5n896c9+U4v04t8xX1HlEAlmD2GBCzIDE2kavuP/E6Fjn9kDch/PItrBQvTWFQ9nLXmQypJakFGWnP/fNEjgEjlzQMWNc9JuFg1qDZzWOZmZLNpy4jJZM0fzPYGTW2qOWMME3d+inZQ00haHKzsCPx7Rm84NhB2lH0oDE/SDKeMm7ZqS5RBsL1BxE/iSvq1bY5x0Cu5qvYgJ/ZoPwBwSzNSHiW3nwMIiqZ0VNeU/VaU+etcGJdfbpHPcpTCHW3kR3i+eKWV4kZsR9ILC2NR3ff5cLu1DVaRfJWGzcLSX66m+LcDeh0atSy8TC4rIG8KirnVxAYKrmc4uRrnOP54pZ9MSOqwuaG+UFLBEziBzEeHVPI2sLe+/SriSW5mt/yqa66cru56NzwqWQL5oTNwa3L19d9inZSsiTjg4czooYxHnIQJq2VDMGA6w3D21tuDz16PJTsmVjrP8hMxmhN9RpIOkMdzNccfop8PFncctgwdJHw7j0WQhIzoHFt1j3HlsxMVoEYJko2EtolKlwdqa522XsoWXeUBmvAK7YKmxtDq+C/wMlzClyQCJICnilueaSYsSpO4gQ3HlniHrqnn+Sa/j45i1gibfbWMF4ujFimS7yPidEdZ5TkRpY3hjYt+XHOv1MIPFPcciZmLM0w7B/6B2MPGBIbKsYkJ4Wxsoo33qkzz8tCHYaKQ28lY4DeQveWoAxyPrLkO8MZ3ni45axJuOKh3HgCGCQeSMbKOUZyd9+GOkDJnjuXWwt6xorU2wdgceuBjVyQciQZB9UzgYZRpzGG/cZOsAut1jZ2EOmez1AyxhsCnQryMwUvRK6SMPCFewbpoNEkRCYq5LLKwjESJxFLTueEBQzSTkjr76P7FKBFzIza8eIan1ViBK1RDyChfWyoCVLt1/OZ3Udoj4DJ/DPyZSzxqbVblLsZOEzJjIazu2vstlU8A11/86D2JNV+XawiOTLVed46/v3fOvDCgpEpY4kYZiAH12+W82ay0h1atdHyE6htvwTl7hOKmh3VntAptRQhwka1h6EwcmQsgeEcYPiR9I+cyVT0LDXsgF0IQLy7jtRjiGoPENwzaYTq/Vem35zGNIm7e2s0TJ2tZOWx8anZchsXs6WlZkOlL3sGkOrbozCJQO3VK6ngJUWlzqR+O5zy6NqBVC3mDUpWk1Fr1fu/1WhLRyEZuPXkYuR1zVnGToRBWsimJoP6ZuK3KRm57LngLgbYB19wGnjH09FsSMDz6AreA0t4EsaWzoMbpJIFL1DC4zBw5ZZmJ3Xisc7GzGaJ02dh1nwz61+vcWFqkUCSAWUGrtzevCP+ICokUHnkKLedrzsJXb5IbaPlTGbLb3rfzsB9W519XgenQgiPTcv2FuUBENLFCxp2VSpZoNI036ISCNn5UC7b9pJTu7RZkKqq4JEQEoQHHMZlzYwnPrFMJVOhkelkLl0pbExax8tuOu/kx5mKhLBrpBVdzgM7hS0Lb+phRQJTyRTJJLhibD/GEgKgz5heRqPKuaYlKkgT6cZSSR+BHcHmstbVpTSVTJfPtTdhOwqXr/F9w+ImGhVz0ZWZupXUPStmHb/lP5UsrxypZDzemKu0rpBafphp3LLspgNCN5fmZbv+6+yzivEyxZbRzVQRmIWrTyUrITCVTMIeYa16R6o7JCRzl6n6uLCRHoeu4ImcCicO2anglDu5qSflbCAeUskQlqQ2diOUnWdpzgeuv+agvLIrrkzqvUuuaULnAyCVzINwu01o59mDl5Ax7jhK7sjiaZCbclm+zYbcEweASiUzL5K12Fj7NycoZIA7nndO14DT8SOtfUenIZma2qSSmdL713XSNsCfS6tDlG+GuOAwPTGFEzFTN8gXcqRywrb3OGfZ4E5f6CNj5QXmdLoi47/g0Km/UyMm1fERavF2QTtpUaHlJ5VMi8mOn1QyQ3J3uL7mIShUIqHAmLbVdzI1pbHrPJXMinNPGcuxzKqKA7/XHEkbE9kYOrvFmQGHcKlkViSnklkxG8nvNcexz8ueT5QgDXJNbwThcw4jlcyqTHcrWe7Spm9uIqTWm/d/Lw6U6WKrzRbJ702dEInXBZZUMpNiOXfzrnD5wfW7e5xrYdK+U6cSnfNH6xbx+rq7MckLlErG4222qtnq+gF+e9wbLsVsVN882qw7P4L/rHKEKvxgSCVTLkT3xqoco3LnHO6vjun9sUvwAs+f+nDognotU8iCLinyN0glU+bc+aB3DpdKJmyXvMILCdy4PGu3kfxl6FSyJUU0A2dpcQ73cOH8nkkrwCHWea8/olBZpiPKlK+LJmVyPuidwzViZsLgx5zmcRmq4FmOUOUAweRMBhJFM3N+iOiG627I3KW0QrpbZ4HcKW+fGbYAyKBCBlLJhAQOl/8cSVauB37riE3056/dLyqCfJ/C78dPxXDXu0r2jEqcxBoRu9Gt92m7MVWj0G/F6sqGUfTa7UQ7HSAtZdJf2h04dw6x5SXZOUeLcMmbBauhfKaSicrx7JBGThxkowt6r5I1kEYCL6I7F/9mIA/oUUckM1/bK6lkooo3StZomOcUMo9VAyubXJT5avFyRFs5yH8nM/B+NPPsQDJcpQXfzFqJvHvcpJLxazmavcrx4XmOLAeynzy7usvPf7oylcyIWKrb7kHvc5uhQgUHrJy3tIi9yU8qGb+aSyV7xIMfAF6JyNgbjB22lDG4dJsN5zpX/6s60I2h1XNJh9sZ8DhntydpAWAyeDmf46CMuSnZG4+dZFpUNn12GcCFB7RMnpMBRQZSyZhk4kpmOpnhMuajZCljzH7KZclAMiBgIJWMQ9771ll78TzNR0o2Qmj9XvRmMwcyToflmmQgGaAwkEpGYatnC+pW890W0qivb9+QOxR6mGin0HMuTwaSgWRgzkAqmbRDQCV7wmgNKFp+pMnn+mQgGUgGAjCQSuZdBOFwJlzunW3GSwaSgWTAnoFUMnuOB2+S1LkqNWxPqTJqMpAMhGcglWxniZrPlhoo83/diTtjJwPJQDIQiYFUskDVSOkKVIyEkgwkA+cwkEp2Tq0SaTKQDCQDyUD385qkJRlIBpKBZCAZOJqBnMmOLl+CTwaSgWQgGfhvKlk2QTKQDCQDycDZDKSSnV2/RJ8MJAPJQDKQSpY9kAwkA8lAMnA2A6lkZ9cv0ScDyUAykAz8PzaFHQ9JbQ8HAAAAAElFTkSuQmCC" width="579" height="303">
<p class="left">17(45)17[18,19] N
<p>Roman adds an additional level of nesting to the loops and pivots in S(11). This is another excellent move that leaves me only one winning reply.
<p>In 2006, Dan Hoey pointed out that a related class of positions containing nested pivot spots “tend to have reasonably large game complexity, since Dawson's Kayles produces nim-values up to *9.” For more on this, see <a href="http://groups.google.com/group/sprouts-theory/browse_thread/thread/9721323bf772ff86#">these</a> <a href="http://groups.google.com/group/sprouts-theory/browse_thread/thread/04e64ff104f47b23#">messages</a> in the “Dawson's Sprouts” thread on sprouts-theory.
<hr><img title="(tPL1LZ)(Pt)(L1)#1^3 + *3 + *2 + *2" class="pos" 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" width="577" height="305">
<p class="right">18(46)19 P
<p>Again, this was the only winning move. Now the game's outcome and its nim-values begin to correspond: the 1<sup>3</sup> component has <a href="http://books.google.com/books?id=ObnlI6vnawAC&lpg=PA426&ots=DCsyoROMJf&dq=%22suppose%20r%20is%20a%20restive%20game%22&pg=PA426#v=onepage&q=%22suppose%20r%20is%20a%20restive%20game%22&f=false">restive</a> nim-values, so we can guess that the position is P if and only if *3 is equal to *3 + *2 + *2, which indeed it is.
<hr><img title="(tPL1LZ)(Pt)(L1)#1^3 + *3 + *2" class="pos" src="data:image/png;base64,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" width="577" height="305">
<p class="left">26(47)41 N
<p>Ordinarily, when you are winning, the answer to an anago in an otherwise-empty region is to convert it to a big loop, but doing that here via 18(47)19 allows four different winning replies, while Roman's move allows only one.
<hr><img title="(tPL1LZ)(Pt)(L1)#1^3 + *3" class="pos" 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" width="584" height="306">
<p class="right">21(48)21[22] P
<p>For the third time in a row, this was the only winning move. Game trees in which two moves in a row have unique winning replies tend to be difficult for humans to analyze, so I can only imagine what a tree with three in a row is like.
<p>This position is clearly P on the basis of its nim-values alone.
<hr><img title="(tPL1LZ)(Pt)(L1)#1^3 + *1" class="pos" 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" width="584" height="306">
<p class="left">2(49)2[3] N
<p>This is another good move; it allows me only two winning replies.
<hr><img title="(tPL1LZ)(Pt)#5^0" class="pos" 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" width="583" height="306">
<p class="right">12(50@13)39 P
<p>This was one of only two winning moves; the other was 17(50)46, which leaves S(11) with nim-values 6<sup>1</sup>.
<p>Roman usually resigns in losing positions with such few remaining live spots. Either the normal-play nim-value of 5 is clouding his vision, or he is doing an excellent job of defending a losing position, by forcing his opponent to play very accurately.
<hr><img title="(tPL1LK)(Pt)#1^2" class="pos" 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" width="583" height="306">
<p class="left">18(51)19 N
<p>Roman plays yet another excellent move which allows me only one winning reply.
<hr><img title="(tPL1[A/A<M>])(Pt)#4^0" class="pos" 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" width="590" height="307">
<p class="right">17(52)18 P
<p>This was the only winning move.
<hr><img title="(tPLL[A/A<M>])(Pt)#1^2" class="pos" 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" width="590" height="307">
<p class="left">20(53)20[45] N
<p>Another strong move that leaves me only two winning replies.
<hr><img title="(tP)(Pt)#4^0" class="pos" 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" width="580" height="308">
<p class="right">16(54@20)44 I P
<p>After this move, S(17) is effectively dead and Roman concedes. This was the simpler of only two winning moves; the other was 19(54@45)46, with nim-values 5<sup>0</sup>.
</div>
<p>Josh Jordan, February, 2011
</body>
</html>
Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com1tag:blogger.com,1999:blog-6387099638018127959.post-74951912168463081462015-12-08T21:57:00.000-08:002015-12-08T22:41:26.925-08:00Advent of Code 2015, Day 9<a href="http://adventofcode.com/day/9">The Day 9 Puzzle of the 2015 Advent of Code</a> asks for the length of the shortest and longest <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">hamiltonian path</a> on a graph. The vertices are cities and the edges between adjacent cities are labelled with the distance between the cities.
<p>Here's a solution <tt>ts.lp</tt> in <a href="https://en.wikipedia.org/wiki/Answer_set_programming">AnsProlog</a> using the <a href="http://potassco.sf.net">Potassco ASP toolkit</a>:
<blockquote><pre>
% The distance relation is symmetric.
dist(B, A, N) :- dist(A, B, N).
% Two cities are "adjacent" if there is a defined distance between them.
adjacent(A, B) :- dist(A, B, _).
% A city exists if it has a distance defined to it from somewhere.
city(A) :- adjacent(A, _).
% Assign a city to each stop on the path from 1..n.
1 { path(N, C): city(C) } 1 :- N = 1..n.
% No city can occur twice in the path.
:- path(N, C), path(M, C), N != M.
% There must be a defined distance between successive cities on the path.
:- path(N, C), path(N+1, D), not adjacent(C, D).
% Minimize the sum of distances between successive cities in the path.
#minimize { X, N : path(N, C), path(N+1, D), dist(C,D,X), N = 1..n }.
#show path/2.
</pre></blockquote>
It requires the following data file <tt>city.lp</tt> as input:
<blockquote><pre>
dist(faerun, norrath, 129).
dist(faerun, tristram, 58).
dist(faerun, alphacentauri, 13).
dist(faerun, arbre, 24).
dist(faerun, snowdin, 60).
dist(faerun, tambi, 71).
dist(faerun, straylight, 67).
dist(norrath, tristram, 142).
dist(norrath, alphacentauri, 15).
dist(norrath, arbre, 135).
dist(norrath, snowdin, 75).
dist(norrath, tambi, 82).
dist(norrath, straylight, 54).
dist(tristram, alphacentauri, 118).
dist(tristram, arbre, 122).
dist(tristram, snowdin, 103).
dist(tristram, tambi, 49).
dist(tristram, straylight, 97).
dist(alphacentauri, arbre, 116).
dist(alphacentauri, snowdin, 12).
dist(alphacentauri, tambi, 18).
dist(alphacentauri, straylight, 91).
dist(arbre, snowdin, 129).
dist(arbre, tambi, 53).
dist(arbre, straylight, 40).
dist(snowdin, tambi, 15).
dist(snowdin, straylight, 99).
dist(tambi, straylight, 70).
city(alphacentauri;arbre;faerun;norrath;snowdin;straylight;tambi;tristram).
#const n = 8.
</pre></blockquote>
Here's the output from running it:
<pre><blockquote>
$ clingo city.lp ts.lp
clingo version 4.4.0
Reading from city.lp ...
Solving...
Answer: 1
path(1,faerun) path(3,norrath) path(8,tristram) path(2,alphacentauri) path(6,arbre) path(5,snowdin) path(4,tambi) path(7,straylight)
Optimization: 391
Answer: 2
path(8,faerun) path(3,norrath) path(5,tristram) path(2,alphacentauri) path(6,arbre) path(1,snowdin) path(4,tambi) path(7,straylight)
Optimization: 387
Answer: 3
path(5,faerun) path(3,norrath) path(8,tristram) path(2,alphacentauri) path(6,arbre) path(1,snowdin) path(4,tambi) path(7,straylight)
Optimization: 341
Answer: 4
path(5,faerun) path(1,norrath) path(6,tristram) path(2,alphacentauri) path(8,arbre) path(3,snowdin) path(4,tambi) path(7,straylight)
Optimization: 308
Answer: 5
path(5,faerun) path(1,norrath) path(8,tristram) path(2,alphacentauri) path(6,arbre) path(3,snowdin) path(4,tambi) path(7,straylight)
Optimization: 274
Answer: 6
path(7,faerun) path(5,norrath) path(1,tristram) path(6,alphacentauri) path(8,arbre) path(3,snowdin) path(2,tambi) path(4,straylight)
Optimization: 269
Answer: 7
path(7,faerun) path(5,norrath) path(8,tristram) path(6,alphacentauri) path(3,arbre) path(1,snowdin) path(2,tambi) path(4,straylight)
Optimization: 248
Answer: 8
path(2,faerun) path(5,norrath) path(1,tristram) path(6,alphacentauri) path(3,arbre) path(7,snowdin) path(8,tambi) path(4,straylight)
Optimization: 218
Answer: 9
path(5,faerun) path(8,norrath) path(1,tristram) path(4,alphacentauri) path(6,arbre) path(3,snowdin) path(2,tambi) path(7,straylight)
Optimization: 207
OPTIMUM FOUND
Models : 9
Optimum : yes
Optimization : 207
Calls : 1
Time : 0.050s (Solving: 0.04s 1st Model: 0.00s Unsat: 0.03s)
CPU Time : 0.040s
</pre></blockquote>
So the shortest path is from Faerun-Norrath-Tristram-AlphaCentauri-Arbre-Snowdin-Tambi-Straylight with a length of 207.
<p>Changing <tt>#minimize</tt> to <tt>#maximize</tt> in <tt>ts.lp</tt> yields a longest path of Norrath-Tristram-AlphaCentauri-Arbre-Snowdin-Tambi-Straylight, with a length of 804.Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-22790360964571518332015-11-20T00:24:00.000-08:002015-11-20T00:25:41.762-08:00Brute-force Sudoku solver in JavaScript<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Brute-force Sudoku solver by Josh Jordan (public domain):</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// https://tentorcupu.wordpress.com/2013/11/08/just-another-extreme-sudoku-solution/</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var coly013= [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 9, 0, 0, 5, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 1, 0, 0, 0, 0, 0, 3, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 2, 3, 0, 0, 7, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 4, 5, 0, 0, 0, 7, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
8, 0, 0, 0, 0, 0, 2, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 6, 4, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 9, 0, 0, 1, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 8, 0, 0, 6, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 5, 4, 0, 0, 0, 0, 7,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// https://tentorcupu.wordpress.com/2013/11/08/just-another-extreme-sudoku-solution/</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var tarx0134 = [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 0, 0, 0, 8,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 3, 0, 0, 0, 4, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 9, 0, 0, 2, 0, 0, 6, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 7, 9, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 6, 1, 2, 0, 0, </div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 6, 0, 5, 0, 2, 0, 7, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 8, 0, 0, 0, 5, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 1, 0, 0, 0, 0, 0, 2, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
4, 0, 5, 0, 0, 0, 0, 0, 3,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var platinum_blonde = [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 0, 0, 1, 2,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 0, 0, 0, 3,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 2, 3, 0, 0, 4, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 1, 8, 0, 0, 0, 0, 5,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 6, 0, 0, 7, 0, 8, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 9, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 8, 5, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
9, 0, 0, 0, 4, 0, 5, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
4, 7, 0, 0, 0, 6, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// "Golden Nugget... accepted by many sources as the world's hardest sudoku</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// puzzle" - http://www.sudokusnake.com/goldennugget.php</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var golden_nugget = [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 0, 0, 3, 9,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 1, 0, 0, 0, 5,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 3, 0, 0, 5, 8, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 8, 0, 0, 9, 0, 0, 6,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 7, 0, 0, 2, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
1, 0, 0, 4, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 9, 0, 0, 8, 0, 5, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 2, 0, 0, 0, 0, 6, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
4, 0, 0, 7, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Arto Inkala's "Hardest Sudoko" from 2010</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// http://www.mirror.co.uk/news/weird-news/worlds-hardest-sudoku-can-you-242294</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var inkala2010 = [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 5, 3, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
8, 0, 0, 0, 0, 0, 0, 2, ,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 7, 0, 0, 1, 0, 5, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
4, 0, 0, 0, 0, 5, 3, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 1, 0, 0, 7, 0, 0, 0, 6,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 3, 2, 0, 0, 0, 8, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 6, 0, 5, 0, 0, 0, 0, 9,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 4, 0, 0, 0, 0, 3, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
0, 0, 0, 0, 0, 9, 7, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Peter Norvig's "hardest (for my program) of the million random puzzles"</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// http://norvig.com/sudoku.html</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var norvig_hard = "000006000059000008200008000045000000003000000006003054000325006000000000000000000".split('').map(function(x) { return +x})</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Peter Norvig's impossible sudoko (has no solutions) from</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// http://norvig.com/sudoku.html</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var norvig_impossible = [</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 0, 0, 5, 0, 8, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 6, 0, 1, 0, 4, 3,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 0, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 1, 0, 5, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 1, 0, 6, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>3, 0, 0, 0, 0, 0, 0, 0, 5,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>5, 3, 0, 0, 0, 0, 0, 6, 1,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 0, 0, 0, 0, 0, 4,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>0, 0, 0, 0, 0, 0, 0, 0, 0,</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
var box_grid;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function initBoxGrid() {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>box_grid = [];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>for (var i = 0; i < 9; i++) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>box_grid[i] = []</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>for (var i = 0; i < 81; i++) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>box_grid[cell_box(i)].push(i);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function solveable(board) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return solveable_r(board.slice(), 80);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function solveable_r(board, i) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
if (box_grid === undefined) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>initBoxGrid();</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (i < 0) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>console.log(board); // show the solution</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return board;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (board[i] > 0) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return solveable_r(board, i-1);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>for (var j = 1; j < 10; j++) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>board[i] = j;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if(valid(board, i) && solveable_r(board, i-1)) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return true;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>board[i] = 0;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return false;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function valid(board, cell) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return valid_row(board, cell_row(cell))</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span> && valid_col(board, cell_col(cell))</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span> && valid_box(board, cell_box(cell));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div>
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Given a cell (0-80), return the number of the row to which it belongs (0-8).</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function cell_row(i) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return Math.floor(i / 9);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Given a cell (0-80), return the number of the column to which it belongs (0-8).</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function cell_col(i) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return i % 9;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
// Given a cell (0-80), return the number of the box to which it belongs (0-8).</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function cell_box(i) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return 3 * Math.floor(cell_row(i) / 3) + Math.floor(cell_col(i) / 3)</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function valid_row(board, row) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
return valid_line(board, row, 9, 1);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function valid_col(board, col) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return valid_line(board, col, 1, 9);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function valid_line(board, row, a, b) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>var seen = 0;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>for (var i = 0; i < 9; i++) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>j = board[row * a + i * b];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (j == 0) continue;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (seen & (1 << j)) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return false;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>seen = seen | (1 << j);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return true;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
function valid_box(board, b) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>var seen = 0;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>for (var i = 0; i < 9; i++) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>j = board[box_grid[b][i]];</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (j == 0) continue;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>if (seen & (1 << j)) {</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return false;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>seen = seen | (1 << j);</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
<span class="Apple-tab-span" style="white-space: pre;"> </span>return true;</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
}</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal; min-height: 13px;">
<br /></div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(coly013));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(platinum_blonde));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(tarx0134));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(golden_nugget));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(inkala2010));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(norvig_hard));</div>
<div style="font-family: Menlo; font-size: 11px; line-height: normal;">
console.log(solveable(norvig_impossible));</div>
<div>
<br /></div>
Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-75392881305510139852015-02-12T22:13:00.000-08:002015-02-20T14:05:13.434-08:000hn0.com solver<img width=300 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">
<p>Below is a solver for the puzzles at <a href="http://0hn0.com">0hn0.com</a>. Using it I calculated that an empty 2x2 puzzle can be solved in 10 different ways, an empty 3x3 puzzle can be solved in 250 different ways, and an empty 4x4 puzzle can be solved in in 22946 different ways.
<pre>
% uses clingo ASP solver from http://potassco.sourceforge.net/
% USAGE: clingo thisfile.txt
% The solution is in the squarecolor(Y,X,blue;red) terms in the output.
% problem specification; example 8x8 puzzle from 0hn0.com:
% - * 6 - 5 - - -
% - * - * - - 5 -
% - - - - - 4 8 -
% 4 - * - * - - -
% - - 5 - * 2 - -
% - - - - - 7 - 3
% 3 - - 7 6 - - -
% begin problem description in ASP
% num(Y,X,N) means the number in square (Y,X) is N
% (squares with numbers are all initially blue.)
% red(Y,X) means square (Y,X) is initially red.
#const ysize=8.
#const xsize=8.
num(1,1,1).
num(1,2,1).
num(1,5,2).
num(1,8,1).
red(2,2).
num(2,3,6).
num(2,5,5).
red(3,2).
red(3,4).
num(3,7,5).
num(4,6,4).
num(4,7,8).
num(5,1,4).
red(5,3).
red(5,5).
num(6,3,5).
red(6,5).
num(6,6,2).
num(7,6,7).
num(7,8,3).
num(8,1,3).
num(8,4,7).
num(8,5,6).
% end ASP problem description
% nothing below this line needs to be edited
% list the valid colors and directions
color(red;blue).
dir(up;down;left;right).
% squares with numbers are blue
squarecolor(Y,X,blue) :- num(Y,X).
% squares specified as red in the initial problem are red in the solution
squarecolor(Y,X,red) :- red(Y,X).
% num(Y,X) :- square(Y,X) was assigned a number in the initial problem
num(Y,X) :- num(Y,X,C).
% choose a color for each initially-empty square
1 { squarecolor(Y,X,C) : color(C) } 1 :- square(Y,X), not num(Y,X), not red(Y,X).
% dir(Y,X,D,YD,XD) = (YD,XD) is 1 square in direction D from (Y,X)
% square 0,0 is used to represent an invalid square, e.g. going up
% from a square in the top row.
row(1..ysize).
col(1..xsize).
square(Y,X) :- row(Y), col(X).
dirok(Y,X, up, Y-1,X) :- square(Y,X).
dirok(Y,X, down, Y+1,X) :- square(Y,X).
dirok(Y,X, left, Y,X-1) :- square(Y,X).
dirok(Y,X, right, Y,X+1) :- square(Y,X).
dir(Y,X,D, 0,0) :- square(Y,X), dir(D), dirok(Y,X,D,YD,XD), not square(YD,XD).
dir(Y,X,D, YD,XD) :- square(Y,X), dir(D), dirok(Y,X,D,YD,XD), square(YD,XD).
% consider any invalid square (0,0) to be colored red.
squarecolor(0,0,red).
% seendir(Y,X,D,N) = N blue squares can be seen in direction D from square (Y,X)
seendir(Y,X,D,1+SD) :- squarecolor(Y,X,blue), dir(D), dir(Y,X,D,YD,XD), seendir(YD,XD,D,SD).
% red squares block vision, so nothing can be seen in any direction from a red square.
seendir(Y,X,D,0) :- squarecolor(Y,X,red), dir(D).
% seen(Y,X,N) = Blue square (Y,X) can see N blue discs in all directions.
seen(Y,X,U+D+L+R-4) :- square(Y,X), squarecolor(Y,X,blue), seendir(Y,X,up,U),
seendir(Y,X,down,D), seendir(Y,X,left,L), seendir(Y,X,right,R).
% each blue square must see at least 1 other blue square (can't see only 0)
:- squarecolor(Y,X,blue), seen(Y,X,0).
% every blue square must see a number of neighbors equal to the number written on it.
:- num(Y,X,C), seen(Y,X,D), C != D.
</pre>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-74247893664047805332015-01-17T01:39:00.002-08:002016-01-11T17:54:11.391-08:00Counting steno strokes<p>How many different strokes are possible on a steno keyboard, using the conventional fingering?
<h3>Background</h3>
<p>The world's fastest typists can type more than <b>200 words per minute</b>, and they all use <a href="http://en.wikipedia.org/wiki/Stenotype">steno keyboards</a>. On these keyboards, it's usual to press more than one key at the same time. The act of pressing one or more keys simultaneously is called a <i>stroke</i>. Each stroke is automatically converted to text by a computer, using a digital dictionary. A particular stroke could represent a letter, a symbol, a word, a phrase, or even an instruction such as "capitalize the next word." To learn more about how steno works, see <a href="http://i.imgur.com/LsKqWBn.png"><i>How court reporting is done</i></a> from the U.S. Bureau of Labor, or watch <a href="https://www.youtube.com/watch?v=Wpv-Qb-dB6g">Plover: Thought to Text at 240 WPM</a> by Mirabai Knight.
<h3>Counting strokes</h3>
<p>How many different strokes are possible? To answer the question, I'll assume that each finger operates independently, count the number of different places each finger can be during a stroke, and multiply those numbers together to get the answer. This way of counting includes an "empty stroke" in which every finger is off the keyboard, but this doesn't count as stroke, so we'll subtract 1 at the end to account for that.
<h3>Steno keyboards and fingers</h3>
<p>A steno keyboard is arranged as in the diagram below. In any particular stroke, each finger can press zero or more keys. Except for the number bar, which we'll deal with below, the conventional fingering assigns each key to one finger. (Some unconventional fingering techniques like the <a href="http://forums.compuserve.com/discussions/The_Court_Reporters/_/_/ws-crforum/67765.9?nav=messages">Philadelphia Shift</a> allow the same key to be pressed by different fingers, but I won't consider them here.)
For some reason, steno keyboards have two keys (both labelled '*') in the 5th column, but in terms of the text that comes out on the screen, it never matters which one of those two is pressed. So in this note, I'll consider the 5th column to have only one key.
<br><img style="margin: 10px" src="data:image/png;base64,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">
<p>The diagram shows the 23 keys of a steno keyboard, with an oval for each finger. A solid red disc in the middle of a key represents the possibility that a finger is pressing only that key. A solid red disc between two keys indicates that a finger can press both keys at once. The right pinky can press 4 keys at once; this is indicated by a solid red disc in the middle of those 4 keys. There is also an empty circle for each finger to represent the possibility that the finger isn't pressing a key.
<h3>Counting the number bar and the left pinky</h3>
<p>The long key at the top of the steno keyboard is called the number bar. For the purposes of counting steno strokes, it doesn't matter which finger presses it. To simplify the counting, and without sacrificing accuracy, we'll assume that if the number bar is pressed, it's pressed by the left pinky. How do we know that it's always possible for the left pinky to press the number bar? Not counting the number bar, the left pinky can be doing one of 2 things: either pressing the key in the first column, or doing nothing. No matter which of those it's doing, it could also be pressing the number key at the same time.
<h3>Counting the other fingers</h3>
<p>Moving on, the left 3rd finger can be doing one of 4 things: (1) pressing the top key in the 2nd column, (2) pressing both keys in the 2nd column, (3) pressing the bottom key in the 2nd column, or (4) not pressing any key. Continuing on like this, we get to the right 1st finger, which can be doing any of 8 things, including pressing the key in the 5th column in various combinations with the top and bottom keys in the 6th column, or not pressing any key. Finally, we get to the right pinky, which can be in any of 10 possible places during a stroke, and the two thumbs, which can each be in any of 4 places.
<h3>And the answer is...</h3>
<p>To count the number of possible strokes, multiply the number of possibilities for each individual finger together, and subtract 1 for the "empty stroke" when no keys are pressed: 4•4•4•4•8•4•4•10•4•4 - 1. That equals 5242879, or around <b>5.25 million</b>.
<h3>Or is it?</h3>
<p>A Google search for ["5242879" steno OR stenotype] turns up no results. Did I made a mistake somewhere? Let me know.Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-79312205507486086882014-11-19T19:56:00.001-08:002015-02-20T14:09:42.576-08:00Ripple Effect<img width=300 src="data:image/png;base64,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">
<p>Here's a solver for Nikoli's <a href="http://en.wikipedia.org/wiki/Ripple_Effect_(puzzle)">Ripple Effect</a> puzzle.
<pre>
% Usage: clingo < rippleffect.lp
%
% Download clingo 4 from http://sourceforge.net/projects/potassco/files/clingo/
% The example puzzle used is from http://en.wikipedia.org/w/index.php?title=Ripple_Effect_(puzzle)&oldid=598393777
% +---+---+---+---+---+---+---+---+---+
% | | | 2 |
% + +---+---+ +---+---+---+---+ +
% | | | | | | | |
% + + +---+---+ + + + +---+
% | | | | | |
% +---+---+---+ +---+---+---+ +---+
% | | | | | |
% +---+---+---+---+ + +---+---+---+
% | | | | 5 | | |
% +---+ + + +---+---+ + + +
% | | | | | |
% + +---+---+---+---+---+---+ +---+
% | | | | | |
% +---+---+---+---+ + +---+---+ +
% | | | | |
% +---+---+---+---+---+---+ + + +
% | 4 | | |
% +---+---+---+---+---+---+---+---+---+
%%% inputs
#const size = 9.
% n(S,N) = square S has number N. (0 for blank)
n(11,0). n(12,0). n(13,0). n(14,0). n(15,0). n(16,0). n(17,0). n(18,0). n(19,2).
n(21,0). n(22,0). n(23,0). n(24,0). n(25,0). n(26,0). n(27,0). n(28,0). n(29,0).
n(31,0). n(32,0). n(33,0). n(34,0). n(35,0). n(36,0). n(37,0). n(38,0). n(39,0).
n(41,0). n(42,0). n(43,0). n(44,0). n(45,0). n(46,0). n(47,0). n(48,0). n(49,0).
n(51,0). n(52,0). n(53,0). n(54,0). n(55,5). n(56,0). n(57,0). n(58,0). n(59,0).
n(61,0). n(62,0). n(63,0). n(64,0). n(65,0). n(66,0). n(67,0). n(68,0). n(69,0).
n(71,0). n(72,0). n(73,0). n(74,0). n(75,0). n(76,0). n(77,0). n(78,0). n(79,0).
n(81,0). n(82,0). n(83,0). n(84,0). n(85,0). n(86,0). n(87,0). n(88,0). n(89,0).
n(91,4). n(92,0). n(93,0). n(94,0). n(95,0). n(96,0). n(97,0). n(98,0). n(99,0).
% r(S,R) = square S is in region R. Region symbols are arbitrary.
r(11,a). r(12,a). r(13,b). r(14,b). r(15,c). r(16,c). r(17,c). r(18,c). r(19,c).
r(21,a). r(22,d). r(23,e). r(24,b). r(25,b). r(26,f). r(27,g). r(28,g). r(29,c).
r(31,a). r(32,d). r(33,d). r(34,d). r(35,b). r(36,f). r(37,g). r(38,g). r(39,g).
r(41,h). r(42,h). r(43,h). r(44,d). r(45,i). r(46,i). r(47,i). r(48,g). r(49,j).
r(51,k). r(52,m). r(53,n). r(54,n). r(55,i). r(56,i). r(57,o). r(58,p). r(59,p).
r(61,q). r(62,m). r(63,n). r(64,n). r(65,o). r(66,o). r(67,o). r(68,p). r(69,p).
r(71,q). r(72,q). r(73,r). r(74,r). r(75,s). r(76,s). r(77,p). r(78,p). r(79,t).
r(81,v). r(82,v). r(83,v). r(84,v). r(85,s). r(86,s). r(87,u). r(88,t). r(89,t).
r(91,w). r(92,w). r(93,w). r(94,w). r(95,u). r(96,u). r(97,u). r(98,t). r(99,t).
%%% Solver
% sz(S,C) = the count of the number of squares in the region enclosing square S is C.
sz(S,C) :- C = #count { T : r(T, R) }, r(S,R).
% row(R) = R is a row index (1..size)
row(1..size).
% col(C) = C is a column index (1..size)
col(1..size).
% sq(Y,X,S) - the square at (Y,X) is S. Example: the square at (3,2) is 32.
sq(Y,X,10*Y+X) :- row(Y), col(X).
% nbetween(A,B,N) = A & B are in the same row or column, with N squares in between them.
nbetween(A,B,X2-X1-1) :- row(Y), col(X1), col(X2), X1 < X2, sq(Y,X1,A), sq(Y,X2,B).
nbetween(A,B,Y2-Y1-1) :- col(X), row(Y1), row(Y2), Y1 < Y2, sq(Y1,X,A), sq(Y2,X,B).
% m(S,N) :- in the solution, square S contains the number N.
m(S,N) :- n(S,N), N != 0.
% chose one value for each initially-empty square that does not exceed the size of its region.
1 { m(S,N) : N = 1..C } 1 :- n(S,0), sz(S,C).
% no duplicate values in the same region.
:- m(S1,N), m(S2,N), r(S1,R), r(S2,R), S1 < S2.
% Whenever the number N occurs twice in the same row or column, there must be at least N squares
% between those two occurrences
:- m(S1,N), m(S2,N), nbetween(S1,S2,M), M < N.
#show m/2.
</pre>
<a name="puzzleparasite"></a>
<hr>
And here's an encoding for the neat puzzle with no numeric clues at <a href="http://puzzleparasite.blogspot.com/2011/12/puzzle-71-ripple-effect.html">http://puzzleparasite.blogspot.com/2011/12/puzzle-71-ripple-effect.html</a>:
<pre>
% size of board
#const size = 8.
% n(S,N) = square S has number N. (0 for blank)
n(11,0). n(12,0). n(13,0). n(14,0). n(15,0). n(16,0). n(17,0). n(18,0).
n(21,0). n(22,0). n(23,0). n(24,0). n(25,0). n(26,0). n(27,0). n(28,0).
n(31,0). n(32,0). n(33,0). n(34,0). n(35,0). n(36,0). n(37,0). n(38,0).
n(41,0). n(42,0). n(43,0). n(44,0). n(45,0). n(46,0). n(47,0). n(48,0).
n(51,0). n(52,0). n(53,0). n(54,0). n(55,0). n(56,0). n(57,0). n(58,0).
n(61,0). n(62,0). n(63,0). n(64,0). n(65,0). n(66,0). n(67,0). n(68,0).
n(71,0). n(72,0). n(73,0). n(74,0). n(75,0). n(76,0). n(77,0). n(78,0).
n(81,0). n(82,0). n(83,0). n(84,0). n(85,0). n(86,0). n(87,0). n(88,0).
% r(S,R) = square S is in region R. Region symbols are arbitrary.
r(11,a). r(12,a). r(13,b). r(14,c). r(15,c). r(16,c). r(17,d). r(18,d).
r(21,a). r(22,b). r(23,b). r(24,e). r(25,f). r(26,c). r(27,d). r(28,d).
r(31,b). r(32,b). r(33,e). r(34,e). r(35,f). r(36,g). r(37,h). r(38,h).
r(41,i). r(42,i). r(43,e). r(44,k). r(45,k). r(46,g). r(47,g). r(48,j).
r(51,m). r(52,n). r(53,n). r(54,k). r(55,k). r(56,o). r(57,g). r(58,j).
r(61,m). r(62,p). r(63,q). r(64,q). r(65,o). r(66,o). r(67,j). r(68,j).
r(71,m). r(72,p). r(73,p). r(74,q). r(75,o). r(76,r). r(77,s). r(78,j).
r(81,m). r(82,m). r(83,p). r(84,p). r(85,r). r(86,r). r(87,r). r(88,r).
</pre>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-37293196892490705732014-11-19T17:36:00.000-08:002015-02-20T14:08:22.157-08:000hh1<img width=300 src="data:image/png;base64,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<p>Here's a solver for the puzzles at <a href="http://0hh1.com">0hh1.com</a>.
<pre>
% USAGE: clingo -n 0 <thisfile.txt # show all solutions to puzzle
%
% Download from: http://sourceforge.net/projects/potassco/files/clingo/3.0.5/
% Two colors: 1 = red, 2 = blue. (0 = empty)
color(1). color(2).
#const size = 6.
% coord(Y,X) = Y,X is a valid coordinate of a cell in the puzzle.
coord(0..size-1,0..size-1).
% p(Y,X,C) = cell [Y,X] is color C in the original puzzle.
%- X X - - -
%O - - - - -
%- - - - - -
%- - - - O -
%- - - - - O
%- X - - - -
color(1). color(2).
#const size = 6.
% coord(Y,X) = Y,X is a valid coordinate of a cell in the puzzle.
coord(0..size-1,0..size-1).
% p(Y,X,C) = cell [Y,X] is color C in the original puzzle.
%- X X - - -
%O - - - - -
%- - - - - -
%- - - - O -
%- - - - - O
%- X - - - -
p(0,0,2). p(0,1,1). p(0,2,0). p(0,3,0). p(0,4,1). p(0,5,2).
p(1,0,1). p(1,1,0). p(1,2,0). p(1,3,2). p(1,4,0). p(1,5,0).
p(2,0,0). p(2,1,2). p(2,2,1). p(2,3,1). p(2,4,2). p(2,5,0).
p(3,0,0). p(3,1,0). p(3,2,2). p(3,3,0). p(3,4,0). p(3,5,0).
p(4,0,1). p(4,1,0). p(4,2,2). p(4,3,1). p(4,4,2). p(4,5,0).
p(5,0,1). p(5,1,2). p(5,2,0). p(5,3,0). p(5,4,2). p(5,5,0).
% q(Y,X,C) = cell[Y,X] is color C in the solved puzzle.
% The colors in the original puzzle must not change in the solution.
q(Y,X,C) :- p(Y,X,C); C != 0.
% Each empty square in the original puzzle must be colored red or blue in the solution.
1 { q(Y,X,C) : color(C) } 1 :- p(Y,X,0).
% f(Y,X) = cell(Y,X) is filled with some color.
f(Y,X) :- q(Y,X,C); C != 0.
% Solution cannot have empty squares.
:- coord(Y,X); not f(Y,X).
% Solution cannot have three adjacent cells of the same color horizontally.
:- q(Y,X,C); q(Y,X+1,C); q(Y,X+2,C).
% Solution cannot have three adjacent cells of the same color vertically.
:- q(Y,X,C); q(Y+1,X,C); q(Y+2,X,C).
% Exactly half of the cells in every row in the solution must be red.
:- coord(Y,_); {coord(Y,X) : q(Y,X,2) } != size/2.
% Exactly half of the cells in every column in the solution must be red.
:- coord(_,X); {coord(Y,X) : q(Y,X,1) } != size/2.
% diffrow(Y1, Y2) = rows Y1 and Y2 differ.
diffrow(Y1, Y2) :- q(Y1,X,C1); q(Y2,X,C2); C1 != C2; coord(Y1,_); coord(Y2,_); Y1 < Y2.
% diffcol(X1, X2) = columns X1 and X2 differ.
diffcol(X1, X2) :- q(Y,X1,C1); q(Y,X2,C2); C1 != C2; coord(_,X1); coord(_,X2); X1 < X2.
% Solution cannot have duplicate rows.
:- coord(Y1,_); coord(Y2,_); Y1 < Y2; not diffrow(Y1, Y2).
% Solution cannot have duplicate columns.
:- coord(_,X1); coord(_,X2); X1 < X2; not diffcol(X1, X2).
</pre>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-52152337322628324672013-12-30T22:16:00.000-08:002015-05-22T02:51:47.348-07:00Mentally calculating the # of Tuesdays between 1700 and 2014This note explains one way to calculate, in your head, the number of Tuesdays between Jan 1, 1700 and Jan 1, 2014. The overall approach is to calculate how many days there were in the years 1700, 1701, 1702, ..., 2014, and then divide by 7 to get the number of weeks, which gives the number of Tuesdays.<br />
<br />
In this note I will talk about some mental tricks/techniques we can use for this, including:<br />
<br />
<ul>
<li>the <a href="http://firstsundaydoomsday.blogspot.com/">First Sunday Doomsday Algorithm</a> for calculating the day of the week for a particular date,</li>
<li>the <a href="http://en.wikipedia.org/wiki/Mnemonic_major_system">mnemonic major system</a> (a.k.a. "<a href="http://folk.ntnu.no/krill/home.htm">pseudonumerology</a>") for remembering intermediate results of calculations,</li>
<li>the method of <a href="http://www.urticator.net/essay/4/497.html">adding the complement of a number rather than subtracting</a>,</li>
<li>the method of <a href="https://www.google.com/search?tbm=bks&hl=en&q=%22casting+out+elevens%22">casting out 11s</a> for error checking, and</li>
<li>the <a href="http://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_by_7">Pohlman-Mass fast test for divisibility by 7</a>.</li>
</ul>
<br />
Let's begin. Overall, there are 2014 - 1700 = 314 years from 1700 to 2014. This works out to 365·314 + <i>L</i> days, where <i>L</i> is the number of leap years in that period.<br />
<br />
The first step is to multiply 365·314. We can simplify this with some basic algebra, by noting that (<i>a</i>+<i>b</i>)(<i>a</i>+<i>c</i>) = <i>a</i>(<i>a</i> + <i>b</i> + <i>c</i>) + <i>bc</i>. Letting <i>a</i> = 300, <i>b</i> = 65, and <i>c</i> = 14, we have: 365·314 = (300 + 65)(300 + 14) = 300(300 + 65 + 14) + (65·14)<br />
= 300·379 + 65·14.<br />
<br />
300·379 isn't too bad to do in your head; it's 900 + 210 + 27 = 1137, and then adding two zeros gives 113700. We will need to remember this number for later. Using the <a href="http://en.wikipedia.org/wiki/Mnemonic_major_system">mnemonic major system</a> we can remember the first four digits 1137 as "toot mic" (picture someone blowing a horn into a microphone).<br />
<br />
Now for 65·14. By writing this as 66·14 - 14, we can use the algebra from above and set <i>a</i> = (66+14)/2 = 40, <i>b</i> = 26, and <i>c</i> = -26, which gives us 66·14 = (40 + 26)(40 - 26) = 40<sup>2</sup> - 26<sup>2</sup>, a difference of two squares. There are many tricks for doing squares. One is that <i>ab</i>^2 = 100<i>a</i><sup>2</sup> + 10·2<i>ab</i> + <i>b</i><sup>2</sup>, so 26<sup>2</sup> = 100·4 + 10·24 + 36 = 400 + 240 + 36 = 676, so 40<sup>2</sup> - 26<sup>2</sup> works out to 1600-676. It is often simpler to calculate <i>x</i> - <i>y</i> by converting it to <i>x</i> + ~<i>y</i>, where ~<i>y</i> is the "<a href="http://www.urticator.net/essay/4/497.html">second complement</a>" of <i>y</i>. Here the second complement of 676 is 324 - 1000, so we have 1600 - 676 = 1600 + (324 - 1000) = 600 + 324 = 924. Finally we subtract 14 to get 65·14 = 910, which we can remember as "pots".<br />
<br />
Now we need to add the last two steps, "toot mic" (113700) and "pots"(910); the sum is 114610, which we can remember as "toot reach toes" (a trumpeter playing a note with the trumpet reaching down to his toes).<br />
<br />
We can check the arithmetic by <a href="https://www.google.com/search?tbm=bks&hl=en&q=%22casting+out+elevens%22">casting out 11s</a>. To do this we first calculate the value of each number mod 11:<br />
<br />
365 = 5 + 3 - 6 = 2 (mod 11)<br />
314 = 4 + 3 - 1 = 6 (mod 11)<br />
114610 = 0 + 6 + 1 - (1 + 4 + 1) = 7 - 6 = 1 (mod 11)<br />
<br />
Then we re-do our original problem of 365·314 using the mod 11 values and make sure the answer is correct:<br />
<br />
365·314 = 2·6 = 12 = 1 = 114610 (mod 11)<br />
<br />
They are equal, so that checks out.<br />
<br />
Now, how many leap years were there in that period? My rule for leap years is this:
<blockquote>If the last two digits of the year are 00, throw them away and keep only the first two digits. Otherwise, keep just the last two digits. Then the year is a leap year just when what remains is divisible by 4.</blockquote>
We can use this rule to figure out that there are 24 leap years in each of the 1700s, 1800s, and 1900s, for a total of 72 leap years in 1700, 1701, 1702, ... 1999. Furthermore, 2000, 2004, 2008, and 2012 were leap years, so in total there were 76 leap years in the 314-year period from Jan 1, 1700 through Jan 1, 2014.<br />
<br />
Our total so far is 114610, "toot reach toes". Adding on 76 days (1 for each leap year) yields 114686, "toot reach fish" (a trumpeter playing for some fishes in the water).<br />
<br />
According to the <a href="http://firstsundaydoomsday.blogspot.com/">First Sunday Doomsday Algorithm</a>, Dec 31, 2014 was a Tuesday, so we need to be sure to include that day in the calculation. In order to make the total number of days equal to an integer number of weeks, we need to end on a Thursday, so we add 2 more days to end on Thursday, Jan 2, 2014. This yields a total of 114688 days, which we can remember as "toot reach fife" (a trumpeter playing up to a fife on a shelf).<br />
<br />
If the above arithmetic is correct, 114688 will equal an integer number of weeks; that is, it will be divisible by 7. It's easy to test for divisibility by 2 or 5, but 7 is a bit trickier. Wikipedia gives a fast method called <a href="http://en.wikipedia.org/wiki/Divisibility_rule#Divisibility_by_7">Pohlman-Mass test for divisibility by 7</a>, which I haven't seen described anywhere else. According to this method, 7 divides 114688 just when 7 divides (114688 - 114114) = 574. And 7 divides 574 just when 7 divides 57 - 4·2 = 49. And since 7 divides 49, 7 also divides 114688, which is consistent with the previous arithmetic being correct.<br />
<br />
Actually carrying out the division mentally, which is kind of a pain, we find that 114688/7 = 16384. It just so happens that this is 2<sup>14</sup>, and so there are 2<sup>14</sup> Tuesdays between Friday, Jan 1, 1700 and Jan 1, 2014.<br />
<br />
For more info on mental calculation, two good books are:<br /><ul>
<li><a href="http://www.myreckonings.com/Dead_Reckoning/Dead_Reckoning.htm">Dead Reckoning: Calculating without Instruments</a>, by Ronald Doerfler<br />
<li><a href="https://www.goodreads.com/book/show/83585.Secrets_of_Mental_Math">Secrets of Mental Math</a>, by Arthur T. Benjamin and Michael Shermer
</ul>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-29515190619416465532013-11-09T11:33:00.002-08:002013-11-09T11:33:14.588-08:00How to interpret probability problems<p>In <a href="http://www.robeastaway.com/blog/tuesday-boy-puzzle">The Irksome Tuesday Boy Problem</a>, Rob Eastaway complains of ambiguity in Gary Foshee's infamous puzzle, which asks: "I have two children, (at least) one of whom is a boy born on a Tuesday - what is the probability that both children are boys?"
<P>I don't get the controversy over this. There's no ambiguity. These problems are meant to be thought of as repeated experiments, like surveys. We want to determine P(2 boys | two children at least one of which is a boy born on Tuesday). So this one becomes:
<ul>
<li>Pick a family at random
<li>"Hello, sir/madam, do you by chance have exactly two children, at least one of which was a boy born on Tuesday?"
<li>If they answer "no", then the interview ends immediately.
<li>Otherwise, ask: "Do you have two boys?"
<li>If "yes", record this call as a "hit"
<li>if "no", record this call as a "miss"
</ul>
<P>After doing lots of these surveys, let <i>h</i> be the number of hits and let <i>m</i> be the number of misses. The desired probability is then <i>h</i>/(<i>m</i>+<i>h</i>).
<p>If the answer depends on some reasonable assumption that is not explicitly stated in the problem, just calculate the answer based on that assumption and make it explicit it to your answer. Example: "The answer is 13/27, provided that the probability of a newborn being a boy is 1/2 and the probability of being born on Tuesday is 1/7."
Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com1tag:blogger.com,1999:blog-6387099638018127959.post-65311335065929914362013-10-28T15:40:00.002-07:002013-10-28T17:32:03.609-07:00The Exponential Lottery Puzzle<p>In this note, I will pose a puzzle about a lottery involving an
exponential number of people. It is my version of a probability
paradox called "The Shooting Room", which was invented by John A.
Leslie in connection with the <a href="http://en.wikipedia.org/wiki/Doomsday_argument">Doomsday Argument</a>. I
will first explain the rules of the lottery and ask whether you should buy a ticket. I will then explain two different ways of thinking about the problem and ask which, if either, is correct.
<p>First, assume that every person is assigned a unique number at birth which doesn't change
throughout the person's lifetime. We'll call this number the person's SSN (social security number). Assume that every person knows his/her own SSN.
<p>Assume that the population grows without bound; that is, there's no specific limit to how large the population can grow. (Let's suppose that humans have become spacefaring and spread out throughout the universe, while still managing to maintain to assign unique SSNs to everyone.)
<p>The lottery has 6 phases:
<ol>
<li>The lottery commission secretly rolls a fair pair of 6-sided dice
until they come up snake eyes (probability 1/36.) Let R be the number
of rolls it took, including the final snake-eyes. If snake eyes are
never rolled, then the lottery never starts.
<li>The lottery commission waits until the population is at least 10^R
(10 to the power R).
<li>The lottery commission makes a list of every person alive in order
from lowest SSN to highest.
<li>The lottery commission informs the first 10^R people on the list
that they are eligible to play.
<li>Each eligible player now decides whether to buy a single ticket.
This decision must be made in isolation; players may not talk about
the lottery. A ticket costs $1.
<li>The first 10^(R-1) people on the list are potential winners. The
lottery commission pays $2 to every potential winner who bought a
ticket.
</ol>
<p>Question: Suppose you have SSN 5055305732 (or whatever), you know the
rules of the lottery, and you have been notified that you are eligible
to play. Should you buy a ticket? What is the expected value?
<p>Here are two ways of thinking about the problem.
<P>On the one hand, (number of potential winners) / (number of people
eligible to play) = 10%. Thus, only 10% of the people who are eligible
to buy a ticket would be winners if they did so. So you shouldn't buy
a ticket.
<p>On the other hand, you effectively became eligible to play on one of
the R dice rolls: the first 10 people on the list were automatically
eligible, then 90 more people became eligible on the first roll if it
wasn't snake eyes, then 900 more people became eligible on the second
roll if it also wasn't snake eyes, and so on. At each roll, the
probability of a later group of people, approximately 10x larger,
becoming eligible is 35/36. If this happens, the people who were
already eligible will be in the first 10%. Thus, the probability that
you are a potential winner, given that you are eligible to play, is
about 35/36. So you should buy a ticket.
<p>Which line of reasoning, if either, is correct?Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com1tag:blogger.com,1999:blog-6387099638018127959.post-35795353177517820572013-06-18T12:21:00.002-07:002016-01-11T18:05:16.450-08:00How to Play Sprouts with Playing Cards<p>It's not much fun to play sprouts with playing cards, but it is possible.
Why would anyone want to do such a thing? Maybe it will be easier to analyze
the game or more straightforward to implement it on a computer this way.
Maybe you're fresh out of pens and paper.
<p>To play a game with <i>N</i> initial spots, you'll need three identical
decks of playing cards
with at least 3<i>N</i>+1 distinct cards in each deck. This way each card will have exactly two identical "twins". (Actually, the cards
are incidental; integers will suffice. This document is really about how to generate legal moves and
update a position represented in Dan Hoey's boundary-list notation.) In the
rules below, we'll assume you've combined the three decks into one large deck.
You will also need a flat space for at least 2<i>N</i>+1 rows of cards. A large
wooden table will do nicely. Each row will contain zero or more stacks of
cards, and each stack will contain one or more cards.
<p>To "cut" a stack of cards means the usual thing: remove one or more cards
from the top of the stack (preserving order) and put them under the
remaining cards in the stack. Here, the player may examine the stack and cut it in any place they choose.
<p>To "play" a card, remove it from the deck and place it in the specified
location.
<h3>Initial position and play</h3>
The initial position consists of <i>N</i> different cards, each in an isolated
stack, all in the same row. Players take turns moving. There are two kinds of moves, joining moves and dividing moves. On his turn, a player must execute either a legal joining move or a legal dividing move, but not both in the same turn. Under the <i>normal play convention</i>, the last player wins. Under the <i>misere play convention</i>, the last player loses.
<h3>Joining moves</h3>
A joining move combines two stacks in the same row. If any step of the move is not possible, the move is illegal.
<ol>
<li>Choose two different nonempty stacks <i>A</i> and <i>B</i> in the same row. Optionally, cut stack <i>A</i>. Optionally, cut stack <i>B</i>.
<li>If <i>A</i> has more than one card, then play a twin of the top card to the bottom of the stack.
<li>If <i>B</i> has more than one card, then play a twin of the top card to the bottom of the stack.
<li>From the deck, remove two identical cards that are not already on the table. Place one on top of <i>A</i>, and one on top of <i>B</i>.
<li>Place A on top of B.
</ol>
<h3>Dividing moves</h3>
A dividing move divides a stack into two stacks, one of which is placed in a
new row. One or more stacks from the original row may be moved to the new row. If any step of the move is not possible, the move is illegal.
<ol>
<li>Choose a nonempty stack. Optionally, cut it.
<li>Play a twin of the top card to the bottom of the stack.
<li>Remove one or more cards -- but not all of them -- from the top of the stack and place them in a new row.
<li>If the original stack or the new stack has more than one card, then play a twin of the the bottom card of the new stack to the top of the original stack.
<li>From the deck, remove two identical cards that are not already on the table. Place one on top of the new stack, and one on top of the original stack.
<li>Optionally, move one or more stacks -- other than the original stack — from the original row to the new row.
</ol>
<h3>Example game</h3>
<p>Consider the following game of 5 moves (in WGOSA notation): 2+ 1(3)2 1(4)2 1(5)4 2(6)3 (see images below)
<p>Here's how that game would be played with cards. To represent the position in text, we will use the following conventions: A stack of
cards is written in order from top card to bottom, with a comma between each
card. A semicolon separates each stack from adjacent stacks in the same row.
A slash separates each row from its neighbors. (This is the notation used by
Dan Hoey in his paper on sprouts notation.)
<table border=0>
<tr><td>(2)<td>initial position:<td>
<ul>
<li>1;2
</ul>
<td><img src="data:image/png;base64,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" width="227" height="129"></tr>
<tr><td>(3)<td>joining move:<td>
<ol>
<li><u>1</u>;<u>2</u>
<li>(skipped)
<li>(skipped)
<li>1<u>,3</u>;2<u>,3</u>
<li>1,3<u>,</u>2,3
</ol>
<td><img src="data:image/png;base64,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" width="229" height="129"></tr>
<tr><td>(4)<td>dividing move:<td>
<ol>
<li>1,3,2,3
<li>1,3,2,3<u>,1</u>
<li>1,3,2<u>/</u>3,1
<li>1,3,2/<u>2,</u>3,1
<li><u>4,</u>1,3,2/<u>4,</u>2,3,1
<li>(skipped)
</ol>
<td><img src="data:image/png;base64,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" width="228" height="128"></tr>
<tr><td>(5)<td>dividing move:<td>
<ol>
<li><u>1,3,2,4</u>/4,2,3,1
<li>1,3,2,4<u>,1</u>/4,2,3,1
<li>1,3,2,4<u>/</u>1/4,2,3,1
<li>1,3,2,4/<u>4,</u>1/4,2,3,1
<li><u>5,</u>1,3,2,4/<u>5,</u>4,1/4,2,3,1
<li>(skipped)
</ol>
<td><img src="data:image/png;base64,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" width="229" height="129"></tr>
<tr><td>(6)<td>dividing move:<td>
<ol>
<li>5,1,3,2,4/5,4,1/<u>2,3,1,4</u>
<li>5,1,3,2,4/5,4,1/2,3,1,4<u>,2</u>
<li>5,1,3,2,4/5,4,1/2,3<u>/</u>1,4,2
<li>5,1,3,2,4/5,4,1/2,3/<u>3,</u>1,4,2
<li>5,1,3,2,4/5,4,1/<u>6,</u>2,3/<u>6,</u>3,1,4,2
<li>(skipped)
</ol>
<td><img src="data:image/png;base64,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" width="232" height="130"></tr>
</table>
<h3>Analogy with graph</h3>
We have represented a plane graph using rows of stacks of cards.
<table border=0>
<tr><th>Playing card term<td>≈<th align=left>Graph theory term
<tr><td>card<td>≈<td>occurrence of vertex in boundary
<tr><td>stack<td>≈<td>left-hand walk of vertices on boundary
<tr><td>row<td>≈<td>face, i.e. set of boundaries
<tr><td>table<td>≈<td>plane graph, i.e. set of faces
</table>
<h3>Credits</h3>
Author: Josh Jordan<br>
Initially published at <a href="http://www.wgosa.org/playingcardssprouts.htm">http://www.wgosa.org/playingcardssprouts.htm</a>
<p>This document builds upon the <a href="http://www.ics.uci.edu/~eppstein/cgt/sprouts.html">sprouts notation system devised by Dan Hoey</a>.Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-36731318502938407002013-04-23T20:10:00.000-07:002013-04-23T20:21:07.927-07:00John Graham-Cunning's Minimum Coin ProblemsIn <a href="http://blog.jgc.org/2013/04/the-minimum-coin-problem-with-prize.html">The Minimum Coin Problem</a>, John Graham-Cunning poses the following problems: <ol>
<li>Given a pile of coins and a target amount, find a way to pay exactly that amount using the maximum number of coins from the pile.
<li>Given a pile of coins and a target amount, find a way to pay at least that amount using the maximum number of coins from the pile, such that removing any coin from the payment yields an amount that is less than the target amount.
<li>Given a pile of coins — each type of coin having a given weight — and a target amount, find a way to pay at least that amount using the maximum weight of coins from the pile, such that removing any coin from the payment yields an amount that is less than the target amount.
</ol>
These can each be posed as integer programming problems and solved with a solver such as GLPK. Here is a <a href="http://pastebin.com/2hB9KWCx">solution to problem 1</a>, a <a href="http://pastebin.com/Dh6NWVaD">solution to problem 2</a>, and a <a href="http://pastebin.com/42dmp4VM">solution to problem 3</a>.Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-44044692200774930702011-09-20T07:37:00.000-07:002018-02-22T16:02:56.040-08:00Open-source answer set solver vs Fico Xpress Optimization SuiteFico's <a href="http://www.fico.com/en/Products/DMTools/Pages/FICO-Xpress-Optimization-Suite.aspx">Xpress Optimization Suite</a> is used by American Airlines, Avis, Honeywell, and the NFL to solve industrial-sized problems in <a href="http://en.wikipedia.org/wiki/Operations_research">operations research</a>.
I was reading one of Fico's white papers, <a href="https://web.archive.org/web/20100826053357/http://www.fico.com/en/FIResourcesLibrary/Xpress_hybridmpcp.pdf">Hybrid MIP/CP solving with Xpress-Optimizer and Xpress-Kalis (May, 2009)</a>, when I came across the following statement about a problem in machine assignment and sequencing.
<br />
<blockquote>
"It is possible to implement this problem entirely either with Xpress-Optimizer or wit
Xpress-Kalis. <i>However, already for this three machines – 12 jobs instance the problem is extremely hard for either technique on its own.</i>" [Section 3.4 ("Results"), page 19, italics mine]</blockquote>
Fico approached this dilemma by creating a hybrid of the solutions for both solvers. The code looked complicated, though, and the problem itself didn't seem that hard. I wanted to see if I was missing something, so I wrote it up in the language of the open-source answer-set solver <a href="http://potassco.org/clingo">Clingo</a>.
<br />
According to the paper, "Optimality is proven within a few seconds on a Pentium IV PC." It takes clingo 3.5 seconds on an Athlon 64 (a similar CPU) to find the same solution. The Xpress-Optimizer+Xpress-Kalis hybrid solution is about 220 lines of code (LOC), while the C<a href="javascript:document.getElementById('clingosol').style.display='block'">lingo solution</a> is about 20 LOC. (*)<br />
<br />
<pre id="clingosol" style="border: solid 1px black; display: none;">#const maxtime = 39.
machine(1..3).
product(1..12).
% table2(P,T1,T2,T3,D1,D2,D3,S,E) :- product P costs C1,C2,and C3 and takes D1,D2,D3
% duration on machines 1,2,3, and must start on or after time S, and must end before time E.
table2(1,12,6,7,10,14,13,2,32).
table2(2,13,6,10,7,9,8,4,33).
table2(3,10,4,6,11,17,15,5,36).
table2(4,8,4,5,6,9,12,7,37).
table2(5,12,6,7,4,6,10,9,39).
table2(6,10,5,6,2,3,4,0,34).
table2(7,7,4,5,10,15,16,3,30).
table2(8,9,5,5,8,11,12,6,26).
table2(9,10,5,7,10,14,13,11,36).
table2(10,8,4,5,8,11,14,2,38).
table2(11,15,8,9,9,12,16,3,31).
table2(12,13,7,7,3,5,6,4,22).
cost(P,1,C1) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
cost(P,2,C2) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
cost(P,3,C3) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
dur(P,1,D1) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
dur(P,2,D2) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
dur(P,3,D3) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
legalworktime(P,S..E-1) :- table2(P,C1,C2,C3,D1,D2,D3,S,E).
% machine(P,M). We choose to build product P on machine M.
% start(P,T). We choose to start building product P at time T.
% Each product is built on exactly one machine.
1 { machine(P, M) : machine(M) } 1 :- product(P).
% Each product starts at exactly one time.
1 { start(P, S) : legalworktime(P,S) } 1 :- product(P).
% machinetime(P,M,T) :- machine is working on product P at time T.
machinetime(P,M,S..S+D-1) :- start(P,S), machine(P,M), dur(P,M,D).
% machinetime(P,T) :- product P is being worked on at time T.
machinetime(P,T) :- machinetime(P,M,T).
:- machinetime(P,M,T), machinetime(Q,M,T), P != Q.
:- machinetime(P,T), not legalworktime(P,T).
% run(P,M,S,E) :- machine is building P at times T, where S ≤ T < E.
% (used only for output)
run(P,M,S,S+D) :- product(P), machine(P,M), start(P,S), dur(P,M,D).
#hide.
#show run/4.
#show cost/1.
% cost(P,C). product P costs $C, given the machine we are making it on
cost(P,C) :- machine(P,M), cost(P,M,C).
totalcost(Cost) :- Cost = #sum [cost(P,C) : product(P) = C].
#minimize [totalcost(Cost) = Cost].
</pre>
According to Section 4 (Summary), "Hybrid solution algorithms need to be developed, implemented, and tested on a case-by-case basis, meaning a considerable investment in terms of development effort and requiring a good understanding of the solution methods and solvers involved."<br />
<br />
Indeed. Or you could just use Clingo.<br />
<br />
<br />
(*) When counting LOC, I ignored lines that consisted only of<br />
<ul>
<li>comments,</li>
<li>code for displaying output,</li>
<li>code for specifying the problem parameters (there were none of these in the Xpress solution), or</li>
<li>code for configuring the solver (there were none of these in the clingo solution).</li>
</ul>
<br />
<br />
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Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com1tag:blogger.com,1999:blog-6387099638018127959.post-79051244688953253822011-03-02T19:44:00.000-08:002016-01-11T18:39:32.794-08:00How I Beat the World Champion at SproutsWith the help of my program Aunt Beast, I won the World Game of Sprouts Association 2010-2011 Tournament in January, 2011. The human world champion requested a follow-up match, billed by WGOSA as the “2011 Clash of the Titans” . As of March, 2011, the match is still ongoing, but in mid-February, I won the first game. <a href="http://www.takingthefun.com/2016/01/2011-sprouts-clash-of-titans-game-1.html">Here’s how I did it</a>.<div><br /></div><div>Update I: I also won game 2. <a href="http://www.takingthefun.com/2016/01/2011-sprouts-clash-of-titans-game-2.html">Here's my analysis.</a></div><div>Update II: I lost game 3, but won game 4. Analysis forthcoming.<br />Update III: I won game 5 and lost game 6, so I won the match. <a href="http://www.wgosa.org/clash2011c.htm">WGOSA has a write-up</a>.<br /></div>Josh Jordanhttp://www.blogger.com/profile/11389483538911210732noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-49313398525916488272010-05-04T17:19:00.000-07:002016-01-11T18:42:30.581-08:00FlowerFinder by William Waite<style>
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">
<p><a href="http://puzzlemist.com/flowerfinder.html">FlowerFinder</a> is a puzzle with only 6 pieces but a rather large state space. One objective is to place them into the frame in two layers so that in each of the 9 circles, exactly 3 petals are visible.<br />
<br />
Each circle can be one of four types, which we will call "top-left", "top-right", "bottom-left", and "bottom-right". We will assign each piece a number from 1 to 6. Each piece is defined as a sequence of three circle types. For example, in the photo, the circles in piece 1, from top to bottom, are of type down-left, up-right, and up-left. Before a piece is placed in the frame, it can (optionally) be flipped horizontally and (optionally) be flipped vertically. We define locations 1,2,3 as the bottom of the frame from left to right, and locations 4,5,6 as the locations in the top of the frame, perpendicular to 1,2,3. Without loss of generality, we can assume that piece 1 is in location 1 or 2, and is not flipped horizontally or vertically. Finally, we require that the petals in each circle in the top row align with the petals in the corresponding circle in the bottom row.<br />
<br />
<pre>$ <a href="http://potassco.sf.net">clingo</a> 0 <a href="javascript:document.getElementById('ff').style.display='block'">flowerfinder.lp</a>
<pre id="ff" style="border: solid 1px black; display: none">
% flowerfinder.lp source
% piece(P) - P is a piece.
% piece(P,A,B,C) - P's circles, in order, are of type A,B, and C.
% piece(P,N,X) - P's Nth circle (1-based) is of type X.
% transform(TransformType,CircleBefore,CircleAfter) - a transformation of
% TransformType changes a circle of type CircleBefore to one of type
% CircleAfter
% align(P,N,Q,M) - when all the pieces are in the frame, circle N of piece P
% aligns with circle M of piece Q.
% fliph(P) - piece P is flipped horizontally before placing it in the frame.
% flipv(P) - piece P is flipped vertically before placing it in the frame.
% fliphed(P,N,X) - after horizontal flipping (if any), the Nth circle of piece P is of type X.
% flipved(P,N,X) - after vertical flipping (if any), the Nth circle of piece P is of type X.
% orientation(P,N,X) - after 90 degree rotation (if any), the Nth circle of piece P is of type X.
% pieceloc(P,L) - piece P is in location L in the frame (1..6).
piece(1..6).
piece(1,downleft,upright,upleft).
piece(2,upright,upleft,upright).
piece(3,downright,upleft,downleft).
piece(4,upright,downleft,upright).
piece(5,downleft,downright,upright).
piece(6,downright,upright,downleft).
piece(P,1,A) :- piece(P,A,B,C).
piece(P,2,B) :- piece(P,A,B,C).
piece(P,3,C) :- piece(P,A,B,C).
transform(fliph,downleft,downright).
transform(fliph,downright,downleft).
transform(fliph,upleft,upright).
transform(fliph,upright,upleft).
transform(flipv,downleft,upleft).
transform(flipv,downright,upright).
transform(flipv,upleft,downleft).
transform(flipv,upright,downright).
transform(rot90,downleft,downright).
transform(rot90,upright,upleft).
transform(rot90,downright,upright).
transform(rot90,upleft,downleft).
align(1,1,4,1).
align(1,2,5,1).
align(1,3,6,1).
align(2,1,4,2).
align(2,2,5,2).
align(2,3,6,2).
align(3,1,4,3).
align(3,2,5,3).
align(3,3,6,3).
% There are as many locations as pieces.
location(P) :- piece(P).
0 { fliph(P) } 1 :- piece(P).
0 { flipv(P) } 1 :- piece(P).
1 { pieceloc(P,L) : location(L) } 1 :- piece(P).
% Without loss of generality, assume piece 1 is in location 1 or 2 (that is,
% on a side or in the middle), and not flipped horizontally or vertically.
:- pieceloc(1, L), L > 2.
:- fliph(1).
:- flipv(1).
% Two different pieces can't be in the same location.
:- pieceloc(P,L),pieceloc(Q,L), P != Q.
% Pieces in locations 4,5,6 are rotated 90 degrees.
rot90(4;5;6).
fliphed(P,N,B) :- piece(P,N,A), transform(fliph,A,B), fliph(P).
fliphed(P,N,A) :- piece(P,N,A), not fliph(P).
flipved(P,4-N,B) :- fliphed(P,N,A), transform(flipv,A,B), flipv(P).
flipved(P,N,A) :- fliphed(P,N,A), not flipv(P).
orientation(P,4-N,B) :- flipved(P,N,A), transform(rot90,A,B), rot90(P).
orientation(P,N,A) :- flipved(P,N,A), not rot90(P).
:- pieceloc(P1,L1), pieceloc(P2,L2), align(L1,C1,L2,C2), orientation(P1,C1,O1), orientation(P2,C2,O2), O1 != O2.
#hide.
#show fliph/1.
#show flipv/1.
#show pieceloc/2.
</pre>
Answer: 1
fliph(3) fliph(5) fliph(6) flipv(2) flipv(3) pieceloc(1,1) pieceloc(2,2) pieceloc(3,3) pieceloc(4,6) pieceloc(5,4) pieceloc(6,5)
SATISFIABLE
Models : 1
Time : 0.020
Prepare : 0.010
Prepro. : 0.000
Solving : 0.010
</pre><br />
So the unique solution is to horizontally flip pieces 3, 5, and 6, vertically flip 2 and 3, put the pieces in the specified locations.<br />
<br />
How large is the state space? The first piece is in one of two locations, and there are 5! ways to place the remaining pieces, 2<sup>5</sup> ways to represent the "horizontally flipped" state of those pieces, and 2<sup>5</sup> ways to represent the "vertically flipped" state of each of those pieces. Finally, the top layer can either be perpendicular to the bottom layer or not. By this reasoning, there are 5! · 2<sup>5</sup> · 2<sup>5</sup> · 2 = 257760 different ways to place the 6 pieces in the frame.joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-28323705883691522342010-04-21T11:53:00.000-07:002010-04-26T08:26:53.213-07:00Pasquale's ProblemPasquale is a self-employed machinist who sells two products: P and Q. The market will accept up to 100 Ps and 100 Qs per week. P sells for $200 and Q sells for $195. The raw materials for each part cost $50. It takes him 18.5 minutes to build a P and 16.5 minutes to build a Q. Pasquale's supplier also sells partially-assembled raw materials for P and Q. The partially-assembled raw materials save him 3 minutes per P and 3.5 minutes per Q, but they also cost more: an additional $25 per P and $29 per Q. Given that Pasquale works at most 40 hours per week, what is Pasquale's maximum weekly profit? For simplicity, assume that the quantity of Ps and Qs he produces each week can be specified by a rational number.<br />
<br />
Calculators are allowed, but solving this without a computer is quite a challenge.<br />
<br />
Here's a hint (rot13): <a href="http://www.rot13.com/index.php?text=Ubj%20zhpu%20jbhyq%20Cnfdhnyr%20or%20noyr%20gb%20znxr%20vs%20ur%20qvqa%27g%20unir%20gur%20bcgvba%20bs%20hfvat%20cnegvnyyl-nffrzoyrq%20enj%20zngrevnyf?">Ubj zhpu jbhyq Cnfdhnyr or noyr gb znxr vs ur qvqa'g unir gur bcgvba bs hfvat cnegvnyyl-nffrzoyrq enj zngrevnyf?</a><br />
<br />
<div id="#pasqualesolution" style="display: none">This problem can be solved quite easily with a linear programming solver, such as the one at <a href="http://www.zweigmedia.com/RealWorld/simplex.html">http://www.zweigmedia.com/RealWorld/simplex.html</a>. Let p and q be the number of Ps and Qs produced each week using only raw materials, and let p' and q' be the number of Ps and Qs produced each week using partially-assembled raw materials.<br />
<br />
<pre>Maximize z = 150p + 125p'+ 145q + 116q' subject to
18.5p + 16.5q + 15.5p' + 13q' <= 2400
p + p' <= 100
q + q' <= 100
Optimal Solution: z = 20581.1; p = 40.5405, p' = 0, q = 100, q' = 0</pre>
So the most Pasquale can make is $20581.10/week. He can do this by avoiding the partially-assembled raw materials entirely, making as many Qs as the market will accept (100), and spending the remainder of his time on Ps (40.5405).
</div><a href="#" onclick="document.getElementById('#pasqualesolution').style.display = 'block'">Click here to view the solution</a>
<p>This puzzle was inspired by a paper by Balakrishnan [1].
<p><p>[1] Balakrishnan, Jaydeep. <u>The theory of constraints and the make-or-buy decision.</u> Journal of Supply Chain Management, January 1, 2005 .joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-34682385771108673002010-04-14T02:15:00.000-07:002016-01-11T18:47:19.214-08:00Nonograms / Paint by Numbers / Griddlers<img 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" style="border: 2px solid black; width: 361; height: 341; float: left; margin-right: 30px">Nonograms / Paint by Numbers / Griddlers are "picture logic puzzles in which cells in a grid have to be colored or left blank according to numbers given at the side of the grid to reveal a hidden picture. In this puzzle type, the numbers measure how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of "4 8 3" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive groups." [<a href="#ref1">1</a>]<br />
<br />
<a href="http://www.chiark.greenend.org.uk/~sgtatham/puzzles/">Simon Tatham's Portable Puzzle Collection</a> has an excellent implementation of these puzzles, under the name "Pattern". They run under Windows, OS X, Linux, and as a Java applet in a browser.<br />
<br />
As usual, the powerful answer set solver <a href="http://potassco.sf.net">clingo</a> makes short work of these puzzles. The source files are:<ul><li><a href="javascript:document.getElementById('mainsrc').style.display='block'">nonogram.lp</a> (clingo input file describing the nonogram puzzle type)<br />
<pre id="mainsrc" style="border: solid 1px black; display: none">
% constraint(Type,N,I,Len) - the Ith group in row/col N must be Len blocks long
% row(Y). Y is a valid row number.
% col(X). X is a valid column number.
% color(X,Y). From a column constraint, we infer that (X,Y) is colored in
% rowcolor(X,Y). From a row constraint, we infer that (X,Y) is colored in
% rowrun(Y,I,X). The Ith run in row Y starts at cell (X,Y).
% colrun(X,I,Y). The Ith run in col X starts at cell (X,Y).
% This following lines simplifies data entry directly into clingo by allowing
% constraints to be entered as a group. This could easily be elminated with
% some pre-processing in, say, Perl.
%
% constraints(col/row,I,A,B,C,...) - The lengths of blocks of filled-in
% cells in column/row I are A,B,C,...
constraint(Type,N,1,A) :- constraints(Type,N,A).
constraint(Type,N,1,A) :- constraints(Type,N,A,B).
constraint(Type,N,1,A) :- constraints(Type,N,A,B,C).
constraint(Type,N,1,A) :- constraints(Type,N,A,B,C,D).
constraint(Type,N,1,A) :- constraints(Type,N,A,B,C,D,E).
constraint(Type,N,1,A) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,1,A) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,2,B) :- constraints(Type,N,A,B).
constraint(Type,N,2,B) :- constraints(Type,N,A,B,C).
constraint(Type,N,2,B) :- constraints(Type,N,A,B,C,D).
constraint(Type,N,2,B) :- constraints(Type,N,A,B,C,D,E).
constraint(Type,N,2,B) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,2,B) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,3,C) :- constraints(Type,N,A,B,C).
constraint(Type,N,3,C) :- constraints(Type,N,A,B,C,D).
constraint(Type,N,3,C) :- constraints(Type,N,A,B,C,D,E).
constraint(Type,N,3,C) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,3,C) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,4,D) :- constraints(Type,N,A,B,C,D).
constraint(Type,N,4,D) :- constraints(Type,N,A,B,C,D,E).
constraint(Type,N,4,D) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,4,D) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,5,E) :- constraints(Type,N,A,B,C,D,E).
constraint(Type,N,5,E) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,5,E) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,6,F) :- constraints(Type,N,A,B,C,D,E,F).
constraint(Type,N,6,F) :- constraints(Type,N,A,B,C,D,E,F,G).
constraint(Type,N,7,G) :- constraints(Type,N,A,B,C,D,E,F,G).
row(1..ymax).
col(1..xmax).
ymax(ymax).
xmax(xmax).
% For each constraint, choose a starting cell for the run.
1 { rowrun(Y,I,X) : col(X) : col(X+Len-1) } 1 :- constraint(row,Y,I,Len).
1 { colrun(X,I,Y) : row(Y) : row(Y+Len-1) } 1 :- constraint(col,X,I,Len).
% Must leave at least one space between two adjacent run.
:- rowrun(N,I,Start1), rowrun(N,J,Start2), constraint(row,N,I,Len), I < J, Start2 < Start1 + Len + 1.
:- colrun(N,I,Start1), colrun(N,J,Start2), constraint(col,N,I,Len), I < J, Start2 < Start1 + Len + 1.
% Infer the color of the cells in each run
color(X,Start..Start+Len-1) :- colrun(X,I,Start), constraint(col,X,I,Len), row(X).
rowcolor(Start..Start+Len-1,Y) :- rowrun(Y,I,Start), constraint(row,Y,I,Len), col(Y).
% The inferred color from the row runs must be the same as those from the column runs.
:- color(X,Y), not rowcolor(X,Y), row(X), col(Y).
:- not color(X,Y), rowcolor(X,Y), row(X), col(Y).
#hide.
#show color/2.
#show xmax/1.
#show ymax/1.
#show constraint/4.
</pre>
<li><a href="javascript:document.getElementById('constraints').style.display='block'">10x10.lp</a> (lists the constraints in the above 10x10 puzzle)<br />
<pre id="constraints" style="border: solid 1px black; display: none">
#const ymax=10. #const xmax=10. #const maxruns=4.
% constraints(col/row,I,A,B,C,...) - The lengths of blocks of filled-in
% cells in column/row I are A,B,C,...
constraints(col,1,1,2,3).
constraints(col,2,1,2).
constraints(col,3,2,5).
constraints(col,4,4).
constraints(col,5,6).
constraints(col,6,6).
constraints(col,7,1,3).
constraints(col,8,8).
constraints(col,9,1).
constraints(col,10,2,3).
constraints(row,1,3).
constraints(row,2,1).
constraints(row,3,3).
constraints(row,4,1,1).
constraints(row,5,1,1,2,1).
constraints(row,6,1,6,1).
constraints(row,7,4,1,1).
constraints(row,8,1,6,1).
constraints(row,9,8).
constraints(row,10,2,4).
</pre>
<li><a href="javascript:document.getElementById('displayer').style.display='block'">display</a> (Perl program to display the solution in human-readable form and check its validity against the original constraints)<br />
<pre id="displayer" style="border: solid 1px black; display: none">
#!/usr/bin/perl
use strict;
use warnings;
while (<>) {
if (/color/) {
my $xmax = 0;
my $ymax = 0;
my @color;
my %constraint;
while(/constraint[(](row|col),(\d+),(\d+),(\d+)/g) {
$constraint{$1}[$2][$3-1] = $4;
}
while(/color[(](\d+),(\d+)/g) {
$color[$1][$2] = 'b';
}
while(/ymax[(](\d+)/g) {
$ymax = $1;
}
while(/xmax[(](\d+)/g) {
$xmax = $1;
}
my $check = checksol(\@color, \%constraint, $xmax, $ymax);
print if $check ne "OK"; # when debugging, show the raw data
foreach my $y (1..$ymax) {
foreach my $x (1..$xmax) {
print $color[$x][$y] && $color[$x][$y] eq 'b' ? 'X' : '.', " ";
print " " if $x % 5 == 0 && $x > 0 && $x < $xmax;
}
print "\n";
print "\n" if $y % 5 == 0 && $y > 0 && $y < $ymax;
}
print "$check\n";
}
else {
print;
}
}
sub checksol {
my ($color, $constraint, $xmax, $ymax) = @_;
foreach my $y (1..$ymax) {
next unless $constraint->{'row'}[$y];
my $row;
foreach my $x (1..$xmax) {
$row .= $color->[$x][$y] || " ";
}
my @counts = map length, $row =~ /(b+)/g;
return "ERROR: row $y: @counts should be @{ $constraint->{'row'}[$y] }"
if "@counts" ne "@{ $constraint->{'row'}[$y] }";
}
foreach my $x (1..$xmax) {
next unless $constraint->{'col'}[$x];
my $col;
foreach my $y (1..$ymax) {
$col .= $color->[$x][$y] || " ";
}
my @counts = map length, $col =~ /(b+)/g;
return "ERROR: column $x: @counts should be @{ $constraint->{'col'}[$x] }"
if "@counts" ne "@{ $constraint->{'col'}[$x] }";
}
return "OK";
}
</pre>
</ul>In this model of the puzzle, the objective is to find the cell in which each unbroken line of filled-in squares ("run") starts, subject to the following constraints:<ul><li>Two runs in the same row or column must be separated by at least one cell of whitespace<br />
<li>From the starting cells and lengths of the runs in a row or column, we can infer which cells in that row or column must be filled in. The set of cells filled in by the row runs must be the same as the set of cells filled in by the column runs.<br />
</ul>Here's the output of solving the above 10x10 puzzle: <pre>$ clingo nonogram.lp 10x10.lp | perl display
Answer: 1
X X X . . . . . . .
. . X . . . . . . .
. . . . . . . X X X
. . . . . . . X . X
X . X . X X . X . .
X . X X X X X X . X
. . X X X X . X . X
X . X X X X X X . X
X X X X X X X X . .
X X . . X X X X . .
OK
SATISFIABLE
Models : 1+
Time : 0.020
Prepare : 0.010
Prepro. : 0.010
Solving : 0.000
</pre>Here's the <a href="http://files.takingthefun.com/nonogram/30x30sol.txt">output from solving a 30x30 puzzle</a>, along with an <a href="http://files.takingthefun.com/nonogram/30x30.png">image</a> of the initial puzzle state and the corresponding <a href="http://files.takingthefun.com/nonogram/30x30.stppc.txt">Simon Tatham's Portable Puzzle Collection save file</a>. <p><p><a name="ref1">[1]</a> Wikipedia, <a href="http://en.wikipedia.org/wiki/Nonogram">Nonogram</a>, (as of Apr. 14, 2010, 08:56 GMT).joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-27150993229620455112010-04-12T09:36:00.001-07:002016-01-11T18:52:03.813-08:00Lunar Lockout<a href="http://www.puzzleworld.org/puzzleworld/app/lunar_lockout/lunar_lockout.htm">Lunar Lockout</a> is similar to a standard <a href="http://en.wikipedia.org/wiki/Sliding_puzzle">sliding puzzle</a>, but with more degrees of freedom. Here's a way to solve Lunar Lockout puzzles using the <a href="http://en.wikipedia.org/wiki/Answer_set_programming">answer set</a> solver <a href="http://potassco.sourceforge.net/">clingo</a>. We'll demonstrate the approach on "Advanced Solitaire Puzzle 1" from the link above.<br />
<img src="data:image/png;base64,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" width="365" height="361"><br />
<br />
This solution uses a main file to specify how the pieces move (<a href="javascript:document.getElementById('lunarlp').style.display='block'">lunar.lp</a>).
<pre id="lunarlp" style="border: solid 1px black; display: none">
% piece(P). P is a piece.
% piece(T,P,X,Y). piece P is at (X,Y) at the end of turn T
% turn(T). T is a turn.
% reachable(T,P,X,Y). It's possible for piece P to be at (X,Y) at the end of turn T
% move(T,P). piece P moves on turn T.
% move(T,P,X,Y). Piece P moves to (X,Y) on turn T.
% direction(D). D is a direction
turn(0..maxturns).
direction(up;down;left;right).
piece(P) :- init(P,X,Y).
piece(T,P) :- piece(T,P,X,Y).
piece(0,P,X,Y) :- init(P,X,Y).
% Four different types of sub-moves
% 1. slide down
reachable(T+1,P,X,YQ+1) :-
reachable(T+1,P,X,Y),
piece(T,X,YQ), not piece(T,P,X,YQ),
[ piece(T,X,Z) : YQ < Z : Z < Y : coordinate(Z) ] 0,
coordinate(X;Y;YQ;YR),
turn(T;T+1),
piece(P),
YQ+1 < Y.
% 2. slide up
reachable(T+1,P,X,YQ-1) :-
reachable(T+1,P,X,Y),
piece(T,X,YQ), not piece(T,P,X,YQ),
[ piece(T,X,Z) : Y < Z : Z < YQ : coordinate(Z) ] 0,
coordinate(X;Y;YQ;YR),
turn(T;T+1),
piece(P),
Y < YQ-1.
% 3. slide right
reachable(T+1,P,XQ-1,Y) :-
reachable(T+1,P,X,Y),
piece(T,XQ,Y), not piece(T,P,XQ,Y),
[ piece(T,Z,Y) : X < Z : Z < XQ : coordinate(Z) ] 0,
coordinate(X;Y;XQ;XR),
piece(P;R),
turn(T;T+1),
X < XQ-1.
% 4. slide left
reachable(T+1,P,XQ+1,Y) :-
reachable(T+1,P,X,Y),
piece(T,XQ,Y), not piece(T,P,XQ,Y),
[ piece(T,Z,Y) : XQ < Z : Z < X : coordinate(Z) ] 0,
coordinate(X;Y;XQ;XR),
piece(P),
turn(T;T+1),
XQ+1 < X.
move(T,P) :- move(T,P,X,Y).
piece(T,X,Y) :- piece(T,P,X,Y).
% One move must be selected at each turn.
1 { move(T,P,X,Y) : piece(P) : coordinate(X;Y) } 1 :-
turn(T),
T > 0.
% A move must be to a reachable location.
:- move(T,P,X,Y), not reachable(T,P,X,Y).
% Can't leave a piece in the same place
:- move(T+1,P,X,Y), piece(T,P,X,Y), turn(T;T+1).
% Ships disappear when they reach the goal.
shipdisappears(T,P) :- move(T,P,X,Y), ship(P), goal(X,Y).
% If a piece is moved to (X,Y), and it's not a ship that disappears on
% that move, then it ends up at (X,Y) a the end of that turn.
piece(T,P,X,Y) :- move(T,P,X,Y), not shipdisappears(T,P).
% Anything that didn't move on a particular turn is in the same place
% at the beginning of the next turn.
piece(T+1,P,X,Y) :-
not move(T+1,P),
piece(T,P,X,Y),
piece(P),
coordinate(X;Y),
turn(T;T+1).
% A piece can stay in the same location to the next turn.
reachable(T+1,P,X,Y) :- piece(T,P,X,Y), turn(T;T+1).
% The puzzle is solved when every ship has disappeared (by reaching
% the goal cell)
notsolved(T) :- piece(T,P), ship(P).
solved :- not notsolved(T), turn(T).
:- not solved.
#hide.
#show move/4.
</pre>
There is also a file to specify the initial location of the pieces for a particular puzzle (<a href="javascript:document.getElementById('advsolitaire1').style.display='block'">advsolitaire1.lp</a>).<br />
<pre id="advsolitaire1" style="border: solid 1px black; display: none">
coordinate(-3..3).
ship(x).
goal(0,0).
init(x,-1,3).
init(1,1,1).
init(2,-1,0).
init(3,2,-1).
init(4,-1,-3).
init(5,0,-3).
</pre>
<br />
Running the solver:<br />
<pre>$ clingo -c maxturns=2 advsolitaire1.lp lunar.lp
Answer: 1
move(1,4,0,-2) move(2,x,0,0)
SATISFIABLE</pre>According to the solver, the puzzle can be solved in two moves, as follows:<ol><li>move piece 4 to (0,-2)<br />
<li>move piece x to (0,0).<br />
</ol>In our coordinate system, the goal is in the center of the grid at (0,0), so the first move locates piece 4 two squares below the goal, and the second move takes the ship home. I challenge anyone to solve "<a href="http://www.puzzleworld.org/puzzleworld/app/lunar_lockout/lunar_lockout.htm">advanced solitaire #30</a>" in the minimum number of moves (18) without using a computer.joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-28863675659076707932010-04-09T18:49:00.000-07:002016-01-11T18:54:42.283-08:00Hinomaru: Japanese Flag Puzzle by Pavel Curtis<img style="float: left; width=240px; height=157px; margin-right: 10px" 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"><a href="http://www.pavelspuzzles.com/2007/08/hinomaru_the_japanese_flag_puz_1.html">Hinomaru</a> is a beautiful puzzle in which "the goal is to put the 12 two-sided domino-shaped pieces into the tray such that the patterns on the face-up sides form a picture of Hinomaru, the Japanese national flag (i.e., a large, solid red disk in the middle of a white field.)".<br />
<br />
It looks temptingly simple: "It's a red disk made out of only 12 pieces, how hard can it be?". But in fact it can be maddeningly difficult to solve by hand. Several of my friends have spent many fruitless hours on this puzzle. It lures you in with its deceptive simplicity, and keeps you going by making it seem that you're always just one piece away from a solution. <br />
<br />
However, the answer set solver <a href="http://potassco.sf.net">clingo</a> makes short work of this puzzle. It took about 30 minutes to program the solution: <a href="javascript:document.getElementById('hinomarulp').style.display='block'">hinomaru.lp</a>.
<pre id="hinomarulp" style="border: solid 1px black; display: none">
% Hinomaru puzzle by Pavel Curtis (http://www.keltis.us/puzzles)
%
% The puzzle consists of 12 2x1 dominoes and a 6x4 board on which to place
% them. We will assign the upper-left square of the board the coordinates
% (1,1). Each domino has two sides, or "faces" as we will call them. Though
% there are 24 total sides, there only 11 distinct faces. The puzzle comes
% with a sheet that identifies each piece with a letter A through L; we will
% adopt that convention here. It quickly becomes apparent that each face has
% only a few possible valid locations. Solving the puzzle is then a matter
% of choosing a face and valid location for each piece such that each square
% of the board is occupied by exactly one piece.
%
% We use the following two predicates to describe the puzzle:
%
% faceloc(Face, Location) - Location is a valid location for Face. A location
% represented by a 4-digit number that specifies the coordinates of the two
% squares occupied by the domino. For example, a Location of 5464, means
% that the domino would occupy the squares (5,4) and (6,4).
%
% pieceface(Piece, Face) - Face is one of the two faces of Piece. For example,
% the two faces of the "I" piece are referred to here as "H0" and "BLANK".
% List the valid locations for each face.
faceloc("A0", 1121;5464).
faceloc("A1", 2122;2434;4151;5354).
faceloc("B1", 1222;5363).
faceloc("BLANK",1112;1213;1314;6162;6263;6364).
faceloc("C0", 2324;2131;4454;5152).
faceloc("C1", 2223;3444;3141;5253).
faceloc("FILL", 3233;3242;3343;4243).
faceloc("G1", 2333;3132;4252;4344).
faceloc("H0", 1424;5161).
faceloc("H1", 2232;3334;4142;4353).
faceloc("L0", 1323;5262).
% List the two faces for each piece.
pieceface("A", "A0";"A1").
pieceface("B", "A0";"B1").
pieceface("C", "C0";"C1").
pieceface("D", "C0";"BLANK").
pieceface("E", "C1";"BLANK").
pieceface("F", "A1";"FILL").
pieceface("G", "A1";"G1").
pieceface("H", "H0";"H1").
pieceface("I", "H0";"BLANK").
pieceface("J", "B1";"FILL").
pieceface("K", "FILL";"G1").
pieceface("L", "L0";"BLANK").
piece(Piece) :- pieceface(Piece, Face).
% For each piece, select one face, and a valid location for that face.
1 {
piecefaceloc(Piece, Face, Loc)
: pieceface(Piece, Face)
: faceloc(Face, Loc)
} 1 :- piece(Piece).
% Each piece uses two squares.
usedsquare(Piece, Loc/100;Loc #mod 100) :-
piecefaceloc(Piece, Face, Loc),
faceloc(Face, Loc),
pieceface(Piece, Face).
% A single square cannot be occupied by two different pieces.
:- usedsquare(Piece1, Square), usedsquare(Piece2, Square), Piece1 != Piece2.
p(Piece, Loc) :- piecefaceloc(Piece, Face, Loc).
#hide.
#show p/2.
</pre>
It is based on the observation that there are only a few locations — usually four, but as few as two and as many as six — where each piece can contribute to the final image. If we place every piece in one of its possible locations, then we will have solved the puzzle.<br />
<br />
Running the solver:<br />
<pre>$ clingo hinomaru.lp
Answer: 1
p("D",6263) p("H",5161) p("F",2122) p("K",2333) p("E",5253) p("G",4344)
p("J",3242) p("C",3141) p("A",2434) p("B",5464) p("I",1112) p("L",1314)
SATISFIABLE
Models : 1+
Time : 0.010
Prepare : 0.000
Prepro. : 0.000
Solving : 0.010
</pre><br />
In this solution, piece "A" occupies squares (2,4) and (3,4), piece "B" occupies squares (5,4) and (6,4), and so forth. I decided not to make solver output which side of each piece faces up, because (a) it's obvious when putting the piece in its location that only one side works in that location, and (b) there are no standard names for the faces (though the puzzle's designer did provide names for the pieces).<br />
<br />
Is the solution really unique up to rearranging face-up pieces? That is, given one solution, is it possible to get another solution by using the other face of one or more pieces? Change the line<br />
<pre>p(Piece, Loc) :- piecefaceloc(Piece, Face, Loc).</pre>to<br />
<pre>p(Piece, Face) :- piecefaceloc(Piece, Face, Loc).</pre>And re-run:<br />
<pre>clingo hinomaru.lp --project 0
Answer: 1
SATISFIABLE
...</pre>There's only one answer set, so the solution is indeed unique.<br />
<br />
How many different ways are there to arrange those faces to create a solution? Change the code back and run:<br />
<br />
<pre>$ clingo --project hinomaru.lp 0
...
Models : 96
...
</pre><br />
While we're at it, in how many different ways could the 12 pieces be arranged on the board, regardless of whether they form a disc or not? First we'll count the number of different ways in which a 6x4 board can be tiled with indistinguishable dominoes which are blank on both sides. I'm sure there's a <a href="http://en.wikipedia.org/wiki/Domino_tiling">better way to do this</a>, but an easy — though computationally inefficient — approach is to use clingo.<br />
<br />
Here's dominoes.lp:<br />
<br />
<pre>#const xmax=6.
#const ymax=6.
#const ndominos=xmax * ymax / 2.
possibleplacement(X,Y,X+1,Y) :- X=1..xmax-1,Y=1..ymax.
possibleplacement(X,Y,X,Y+1) :- X=1..xmax,Y=1..ymax-1.
square(X,Y) :- X=1..xmax,Y=1..ymax.
% Select the valid placements.
ndominos { placement(X1,Y1,X2,Y2) : possibleplacement(X1,Y1,X2,Y2) } ndominos.
% Each placement uses two squares.
coveredsquare(X1,Y1) :- placement(X1,Y1,X2,Y2).
coveredsquare(X2,Y2) :- placement(X1,Y1,X2,Y2).
% There must be no uncovered squares.
:- square(X,Y), not coveredsquare(X,Y).
#hide. #show placement/4.
</pre><br />
Running the solver:<br />
<br />
<pre>$ clingo dominoes.lp 0
...
Models : 281
...
</pre><br />
Okay, so for each of those 281 ways to tile the board with dominoes, we can replace the dominoes with puzzle pieces in 12! ways, and we can choose which sides are face up in 2<sup>12</sup> ways. Now 281 · 12! · 2<sup>12</sup> is about 5.5 · 10<sup>14</sup>, so good luck trying to solve Hinomaru by placing pieces randomly!joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0tag:blogger.com,1999:blog-6387099638018127959.post-78383858326806352662010-04-04T20:29:00.000-07:002010-04-12T14:09:33.423-07:00Mathcounts 1999 National Competition Sprint Problem 4<style>
pre { font-size: large }
</style><br />
A fly starts at one vertex of a cube with edge length 1 inch and randomly walks along edges of the cube. What is the number of inches in the longest distance that it could walk without retracing any edge?<br />
<br />
cube.lp:<blockquote><pre>% 5--6
% / /|
% 1--2 7
% | |/
% 3--4
e(1,2;5;3).
e(2,1;4;6).
e(3,1;4;8).
e(4,3;2;7).
e(5,1;6;8).
e(6,5;2;7).
e(7,4;6;8).
e(8,3;5;7).
#const nedges = 12.</pre></blockquote><br />
<br />
longestpath.lp:<blockquote><tt><br />
% Find a longest path in an undirected graph, where length = number of edges in path.<br />
<br />
% e(X,Y) - There is an undirected edge from X to Y.<br />
% edge(X,Y) - e(X,Y) plus e(Y,X).<br />
% path(N,X,Y) - step N of the path takes the edge (X,Y).<br />
<br />
edge(Y,X) :- e(X,Y).<br />
edge(X,Y) :- e(X,Y).<br />
<br />
% Any edge could be the first.<br />
1 { path(1,X,Y) : edge(X,Y) } 1.<br />
<br />
% Subsequent edges must start at the ending vertex of the previous edge.<br />
0 { path(N+1,Y,Z) : edge(Y,Z) } 1 :- path(N, X,Y), edge(X,Y), N=1..nedges.<br />
<br />
% A path must not repeat a previous edge.<br />
:- path(N,Y,Z), path(M,Y,Z), N < M.<br />
:- path(N,Y,Z), path(M,Z,Y), N < M.<br />
<br />
#maximize [ path(N,X,Y) : N = 1..nedges : edge(X,Y) ].<br />
<br />
#hide.<br />
#show path/3.<br />
#show length/1.</tt></blockquote><br />
<br />
display:<blockquote><pre>#!/usr/bin/perl -w
use strict;
my @path;
while (<>) {
if (/path/) {
@path = ();
while (/path[(](\d+),(\d+),(\d+)[)]/g) {
$path[$1-1] = "($2,$3)";
}
}
}
print "@path [length=", scalar(@path), "]\n";
</pre></blockquote><br />
<br />
Running it:<br />
<blockquote><tt>$ clingo cube.lp longestpath.lp | perl display<br />
(1,2) (2,6) (6,5) (5,1) (1,3) (3,4) (4,7) (7,8) (8,5) [length=9]<br />
</tt></blockquote>joshjordanhttp://www.blogger.com/profile/14574896378764750526noreply@blogger.com0