Backtracking for this problem consists of choosing some order of the matrix elements and recursively placing ones or zeros, while checking that in every row and column the number of elements that have not been assigned plus the number of ones or zeros are both at least . While more sophisticated than brute force, this approach will visit every solution once, making it impractical for larger than six, since the number of solutions is already 116,963,796,250 for  = 8, as we shall see.