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<h1 class="puzTitle">The Schoolgirl Problem Puzzle - Solution</h1><div class="puzPuzzle"><h2>The Puzzle:</h2><div class="puzText"><div class="puzThumb"><a href="logic-puzzles-index.html"><img src="images/walk.svg" alt="The Schoolgirl Problem" style="border-style: none" /></a></div>In a boarding school there are fifteen schoolgirls who always take their daily walks in groups of three. <br />
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How can it be arranged so that each schoolgirl walks in a group with two different companions every day for a week (7 days)?</div></div><div class="puzSep"></div><div class="puzSoln"><h2>Our Solution:</h3><div class="puzSolnText">Give the girls letters A to O - one possible schedule is then:<br />
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<pre>Sun Mon Tues Wed Thu Fri Sat
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AFK ABE BCF EFI CEK EGM KMD
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BGL CDG DEH GHK DFL FHN LNE
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CHM HIL IJM LMA GIO IKB OBH
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DIN JKN KLO NOC HJA JLC ACI
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EJO MOF NAG BDJ MNB OAD FGJ
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</pre><br />
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<br />
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The famouse Schoolgirls Problem was first posed by Reverend Thomas Kirkman in 1857. It led to a new branch of mathematics called Combinatorics. <br />
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The problem has since been described as a specific example of a Steiner Triple System. Numerous methods of solution exist, but Trial and Error still (just!) works, but you must be patient!</div></div><div class="puzSolnFtr">See this puzzle <a href="the-schoolgirl-problem.html">without solution</a><br />Discuss this puzzle at the <a href="http://www.mathisfunforum.com/index.php">Math is Fun Forum</a></div><div class="related"><a href="logic-puzzles-index.html">Logic Puzzles</a><a href="index.html">Puzzles Index</a></div><!-- #EndEditable --></div>
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