A chess tableau is a standard Young tableau (SYT) in which orthogonally
adjacent entries have opposite parity. Remarkably, the number of 3xn
chess tableaux is the same as several other quantities: the number of
3x(n-1) nonconsecutive tableaux (SYT in which i and i+1 never appear in
the same row), the Charney-Davis statistic of a 3xn shape, and the number
of Baxter permutations of n. Yet there is no obvious bijection between
any two of these. Our main result is a pleasant but mysterious bijection
between chess tableaux and nonconsecutive tableaux with three rows.
Bijections with the Charney-Davis statistic remain an open problem.

Our original motivation was, appropriately enough, composing chess
problems. In the last part of the talk we present and explain two chess
problems (one by Noam Elkies) that are related to chess tableaux. The
problems have the same flavor as the chess problems in Stanley's book EC2.

The definition of a Young tableau and (for the last part of the talk)
knowledge of how chess pieces move are sufficient background for the
talk; other terminology will be explained.

This is joint work with Ken Fan and Henrik Eriksson.