prob029: Prime queen attacking problem

proposed by

A possible encoding as a maxCSP:

variables:

a variable V_i for each number i in {1,...,n^2} and

a variable Q for the queen.

domains:

the domains of all these variables are the possible cells on the n x n chessboard.

hard constraints:

an alldiff constraint on the n^2 V_i variables.

for each pair V_i, V_{i+1} of variables, a binary constraint allowing only the pairs of cells being the start and end of a knight move.

soft constraints:

for each prime p, a binary constraint involving Q and V_p, allowing only the pairs of cells being the start and end of a queen move.

goal:

minimize the number of soft constraints violated.