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project_euler/pe/p045.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 45 - Project Euler</title>
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<h2>Triangular, pentagonal, and hexagonal</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 45</h3><span style="width:300px;color:#666;">Published on Friday, 6th June 2003, 06:00 pm; Solved by 33631</span></div>
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<div class="problem_content" role="problem">
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<p>Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:</p>
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<table>
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<tr>
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<td>Triangle</td>
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<td> </td>
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<td>T<sub><i>n</i></sub>=<i>n</i>(<i>n</i>+1)/2</td>
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<td> </td>
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<td>1, 3, 6, 10, 15, ...</td>
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</tr>
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<tr>
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<td>Pentagonal</td>
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<td> </td>
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<td>P<sub><i>n</i></sub>=<i>n</i>(3<i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='−' border='0' style='vertical-align:middle;' />1)/2</td>
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<td> </td>
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<td>1, 5, 12, 22, 35, ...</td>
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</tr>
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<tr>
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<td>Hexagonal</td>
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<td> </td>
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<td>H<sub><i>n</i></sub>=<i>n</i>(2<i>n</i><img src='images/symbol_minus.gif' width='9' height='3' alt='−' border='0' style='vertical-align:middle;' />1)</td>
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<td> </td>
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<td>1, 6, 15, 28, 45, ...</td>
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</tr>
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</table>
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<p>It can be verified that T<sub>285</sub> = P<sub>165</sub> = H<sub>143</sub> = 40755.</p>
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<p>Find the next triangle number that is also pentagonal and hexagonal.</p>
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</div><br />
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