Open chess positions
Problem 628
A position in chess is an (orientated) arrangement of chess pieces placed on a chessboard of given size. In the following, we consider all positions in which pawns are placed on a board in such a way, that there is a single pawn in every row and every column.
We call such a position an open position, if a rook, starting at the (empty) lower left corner and using only moves towards the right or upwards, can reach the upper right corner without moving onto any field occupied by a pawn.
Let be the number of open positions for a chessboard.
For example, , illustrated by the two open positions for a chessboard below.
For example, , illustrated by the two open positions for a chessboard below.
You are also given .
Find modulo .