The NN-queens Problem on a symmetric Toeplitz matrix

We consider the problem of placing nn nonattacking queens on a symmetric n×nn×n Toeplitz matrix. As in the NN-queens Problem on a chessboard, two queens may attack each other if they share a row or a column in the matrix. However, the usual diagonal restriction is replaced by specifying that queens may attack other queens that occupy squares with the same number value in the matrix. We will show that nn nonattacking queens can be placed on such a matrix if and only if n≡0,1mod4n≡0,1mod4.