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project_euler/pe/p075.html
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project_euler/pe/p075.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 75 - Project Euler</title>
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<h2>Singular integer right triangles</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 75</h3><span style="width:300px;color:#666;">Published on Friday, 30th July 2004, 06:00 pm; Solved by 8053</span></div>
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<div class="problem_content" role="problem">
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<p>It turns out that 12 cm is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples.</p>
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<p style='margin-left:50px;'><b>12 cm</b>: (3,4,5)<br />
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<b>24 cm</b>: (6,8,10)<br />
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<b>30 cm</b>: (5,12,13)<br />
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<b>36 cm</b>: (9,12,15)<br />
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<b>40 cm</b>: (8,15,17)<br />
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<b>48 cm</b>: (12,16,20)</p>
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<p>In contrast, some lengths of wire, like 20 cm, cannot be bent to form an integer sided right angle triangle, and other lengths allow more than one solution to be found; for example, using 120 cm it is possible to form exactly three different integer sided right angle triangles.</p>
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<p style='margin-left:50px;'><b>120 cm</b>: (30,40,50), (20,48,52), (24,45,51)</p>
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<p>Given that L is the length of the wire, for how many values of L <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 1,500,000 can exactly one integer sided right angle triangle be formed?</p>
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