Problems with inadmissible squares are very easy to handle with the direct method using reduced matrices for solutions with xij > 0. It is only necessary to fix xij = 0 for every inadmissible square. This can be accomplished by making the cij for each inadmissible square so large that the subtractions of the reduction process never reduce it to zero. Operationally this can be managed by placing an X in each inadmissible square and using an X in the next matrix when a constant is subtracted. Of course there may be so many inadmissible squares that no solution is possible but this method of reduced matrices then reveals the fundamental inconsistency since eventually the reduction process leads to some delta = X which can not be used in a transformation.