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puzzles/project_euler/pe/p194.html
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puzzles/project_euler/pe/p194.html
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="utf-8" />
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<meta name="author" content="Colin Hughes" />
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<meta name="description" content="A website dedicated to the fascinating world of mathematics and programming" />
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<meta name="keywords" content="programming,mathematics,problems,puzzles" />
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<title>Problem 194 - Project Euler</title>
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<link rel="shortcut icon" href="http://projecteuler.net/favicon.ico" />
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<link rel="stylesheet" type="text/css" href="style_main.css" />
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<link rel="stylesheet" type="text/css" href="style_light.css" />
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<div id="info_panel"><a href="rss2_euler.xml"><img src="images/icon_rss.png" alt="RSS Feed" title="RSS Feed" /></a><a href="secure=c9c2b"><img src="images/icon_lock.png" alt="Use secure connection" title="Use secure connection" /></a></div>
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<div style="text-align:center;" class="print"><img src="images/pe_banner.png" alt="projecteuler.net" style="border:none;" /></div>
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<h2>Coloured Configurations</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 194</h3><span style="width:300px;color:#666;">Published on Saturday, 17th May 2008, 10:00 am; Solved by 741</span></div>
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<div class="problem_content" role="problem">
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<p>Consider graphs built with the units A: <img src="project/images/p_194_GraphA.png" style="vertical-align:middle;" alt="" />
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and B: <img src="project/images/p_194_GraphB.png" style="vertical-align:middle;" alt="" />, where the units are glued along
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the vertical edges as in the graph <img src="project/images/p_194_Fig.png" style="vertical-align:middle;" alt="" />.</p>
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<p>A configuration of type (<var>a</var>,<var>b</var>,<var>c</var>) is a graph thus built of <var>a</var> units A and <var>b</var> units B, where the graph's vertices are coloured using up to <var>c</var> colours, so that no two adjacent vertices have the same colour.<br />
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The compound graph above is an example of a configuration of type (2,2,6), in fact of type (2,2,<var>c</var>) for all <var>c</var> <img src='images/symbol_ge.gif' width='10' height='12' alt='≥' border='0' style='vertical-align:middle;' /> 4.</p>
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<p>Let N(<var>a</var>,<var>b</var>,<var>c</var>) be the number of configurations of type (<var>a</var>,<var>b</var>,<var>c</var>).<br />
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For example, N(1,0,3) = 24, N(0,2,4) = 92928 and N(2,2,3) = 20736.</p>
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<p>Find the last 8 digits of N(25,75,1984).</p>
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</div><br />
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<br /></div>
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