We say that n squares in a n×n board are scattered if no two of them are in the same row or column.In every square of this board is witten a natural number so that the sum of numbrs in n scattered squares is always the same
and no row or no column contains two equal numbers .It turned out that the numbers on the main diagonal are arranged in the increasing order ,and that their product is the smallest among all products of n scattered numbers .Prove that scattered numbers with the greatest product are exactly those on the other diagonal. combinatorics unsolvedcombinatorics