IMO 1985 LL TUR80

Origin: TUR

Problem

Let E = {1, 2, . . ., 16} and let M be the collection of all 4 \times 4 matrices whose entries are distinct members of E. If a matrix A = (aij)4\times4 is chosen randomly from M, compute the probability p(k) of maxi minj aij = k for k \inE. Furthermore, determine l \inE such that p(l) = max{p(k) | k \inE}.