MathDB
12 couples on a circle, swapping

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April 23, 2009

Problem Statement

Twelve couples are seated around a circular table such that all of men are seated side by side, and every women are seated to opposite of her husband. In every step, a woman and a man next to her are swapping. What is the least possible number of swapping until all couples are seated side by side?
<spanclass=latexbold>(A)</span> 36<spanclass=latexbold>(B)</span> 55<spanclass=latexbold>(C)</span> 60<spanclass=latexbold>(D)</span> 66<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ 36 \qquad<span class='latex-bold'>(B)</span>\ 55 \qquad<span class='latex-bold'>(C)</span>\ 60 \qquad<span class='latex-bold'>(D)</span>\ 66 \qquad<span class='latex-bold'>(E)</span>\ \text{None}