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project_euler/pe/p116.html
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project_euler/pe/p116.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 116 - Project Euler</title>
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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>Red, green or blue tiles</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 116</h3><span style="width:300px;color:#666;">Published on Friday, 3rd March 2006, 06:00 pm; Solved by 5761</span></div>
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<div class="problem_content" role="problem">
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<p>A row of five black square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), green (length three), or blue (length four).</p>
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<p>If red tiles are chosen there are exactly seven ways this can be done.</p>
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<td> </td>
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<p>If green tiles are chosen there are three ways.</p>
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<td> </td>
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<p>And if blue tiles are chosen there are two ways.</p>
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<p>Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of replacing the black tiles in a row measuring five units in length.</p>
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<p>How many different ways can the black tiles in a row measuring fifty units in length be replaced if colours cannot be mixed and at least one coloured tile must be used?</p>
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<p class="info">NOTE: This is related to problem <a href="index.php?section=problems&id=117">117</a>.</p>
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</div><br />
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