Mathematical background

NumberCrunch is originated from group-theory. It has been proved, that there is always a solution for all matrices greater or equal to 3 x 3. But for a matrix 2 x 2, 3 x 2, 2 x 3, 2 x >=4, >= 4 x 2, only one sixth of the possible positions do have a solution.
Concerning the game, there will always be a solution because the positions are calculated from the solution backwards.