MathDB

15

Part of 1998 National Olympiad First Round

Problems(1)

12 couples on a circle, swapping

Source: 0

4/23/2009
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=′latex−bold′>(A)</span> 36<spanclass=′latex−bold′>(B)</span> 55<spanclass=′latex−bold′>(C)</span> 60<spanclass=′latex−bold′>(D)</span> 66<spanclass=′latex−bold′>(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}