Let M1,M2,....,M(n-1) be a set of mutually orthogonal latin squares of order n. if i and p are not equal, and j and q are are not equal (ie: not talking about the same entry), prove that the cells (i,j) and (p,q) are occupied by the same symbol in exactly one of the latin squares.
Im not sure where to go with this, im thinking use the fact that since there are n-1 mutually orthogonal latin squares then there is an affine plane of order n.