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puzzles/project_euler/pe/p115.html
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puzzles/project_euler/pe/p115.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="keywords" content="programming,mathematics,problems,puzzles" />
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<title>Problem 115 - Project Euler</title>
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<h2>Counting block combinations II</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 115</h3><span style="width:300px;color:#666;">Published on Friday, 24th February 2006, 06:00 pm; Solved by 4774</span></div>
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<div class="problem_content" role="problem">
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<p class="info">NOTE: This is a more difficult version of problem <a href="index.php?section=problems&id=114">114</a>.</p>
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<p>A row measuring <i>n</i> units in length has red blocks with a minimum length of <i>m</i> units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one black square.</p>
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<p>Let the fill-count function, F(<i>m</i>, <i>n</i>), represent the number of ways that a row can be filled.</p>
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<p>For example, F(3, 29) = 673135 and F(3, 30) = 1089155.</p>
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<p>That is, for <i>m</i> = 3, it can be seen that <i>n</i> = 30 is the smallest value for which the fill-count function first exceeds one million.</p>
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<p>In the same way, for <i>m</i> = 10, it can be verified that F(10, 56) = 880711 and F(10, 57) = 1148904, so <i>n</i> = 57 is the least value for which the fill-count function first exceeds one million.</p>
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<p>For <i>m</i> = 50, find the least value of <i>n</i> for which the fill-count function first exceeds one million.</p>
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