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puzzles/project_euler/pe/p242.html
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puzzles/project_euler/pe/p242.html
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<title>Problem 242 - Project Euler</title>
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<h2>Odd Triplets</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 242</h3><span style="width:300px;color:#666;">Published on Saturday, 25th April 2009, 06:00 am; Solved by 633</span></div>
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<div class="problem_content" role="problem">
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<p>Given the set {1,2,...,<var>n</var>}, we define <var>f</var>(<var>n</var>,<var>k</var>) as the number of its <var>k</var>-element subsets with an odd sum of elements. For example, <var>f</var>(5,3) = 4, since the set {1,2,3,4,5} has four 3-element subsets having an odd sum of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.</p>
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<p>When all three values <var>n</var>, <var>k</var> and <var>f</var>(<var>n</var>,<var>k</var>) are odd, we say that they make <br />
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an <i>odd-triplet</i> [<var>n</var>,<var>k</var>,<var>f</var>(<var>n</var>,<var>k</var>)].</p>
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<p>There are exactly five odd-triplets with <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 10, namely:<br />
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[1,1,<var>f</var>(1,1) = 1], [5,1,<var>f</var>(5,1) = 3], [5,5,<var>f</var>(5,5) = 1], [9,1,<var>f</var>(9,1) = 5] and [9,9,<var>f</var>(9,9) = 1].</p>
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<p>How many odd-triplets are there with <var>n</var> <img src='images/symbol_le.gif' width='10' height='12' alt='≤' border='0' style='vertical-align:middle;' /> 10<sup>12</sup> ?</p>
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