MathDB

At a dance there are

12

men, numbered

1

12

, and

12

women numbered

1

12

. Each man is assigned a “secret friend” among the

11

others. They all danced all the pieces. In the first piece each man danced with the woman who has the same number. From then on, each man danced the new piece with the woman who had danced the piece earlier with his secret friend. In the third piece the couples were: https://cdn.artofproblemsolving.com/attachments/c/d/f5ea0931e5751739c1ba556f84ab5736f2d11a.png Find the number of each man's secret friend.

Problem Statement