MathDB

In a dancing hall, there are

n

girls standing in one row and

n

boys in the other row across them (so that all

2n

dancers form a

2 \times n

board). Each dancer gives her / his left hand to a neighboring person standing to the left, across, or diagonally to the left. The analogous rule applies for right hands. No dancer gives both hands to the same person. In how many ways can the dancers do this?

Problem Statement