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puzzles/project_euler/pe/p275.html
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puzzles/project_euler/pe/p275.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 275 - Project Euler</title>
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<h2>Balanced Sculptures</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 275</h3><span style="width:300px;color:#666;">Published on Friday, 22nd January 2010, 05:00 pm; Solved by 415</span></div>
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<div class="problem_content" role="problem">
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<p>Let us define a <i>balanced sculpture</i> of order <var>n</var> as follows:
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<ul>
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<li>A <dfn title="An arrangement of identical squares connected through shared edges; holes are allowed.">polyomino</dfn> made up of <var>n</var>+1 tiles known as the <i>blocks</i> (<var>n</var> tiles)<br /> and the <i>plinth</i> (remaining tile);</li>
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<li>the plinth has its centre at position (<var>x</var> = 0, <var>y</var> = 0);</li>
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<li>the blocks have <var>y</var>-coordinates greater than zero (so the plinth is the unique lowest tile);</li>
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<li>the centre of mass of all the blocks, combined, has <var>x</var>-coordinate equal to zero.</li>
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</ul></p>
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<p>When counting the sculptures, any arrangements which are simply reflections about the <var>y</var>-axis, are <u>not</u> counted as distinct. For example, the 18 balanced sculptures of order 6 are shown below; note that each pair of mirror images (about the <var>y</var>-axis) is counted as one sculpture:</p>
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<div align='center'><img src="project/images/p_275_sculptures2.gif" /></div>
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<p>There are 964 balanced sculptures of order 10 and 360505 of order 15.<br />How many balanced sculptures are there of order 18?</p>
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