A board n×n is divided into n2 unit squares and a number is written in each unit square.
Such a board is called interesting if the following conditions hold:
∘ In all unit squares below the main diagonal, the number 0 is written;
∘ Positive integers are written in all other unit squares.
∘ When we look at the sums in all n rows, and the sums in all n columns, those 2n numbers
are actually the numbers 1,2,...,2n (not necessarily in that order).a) Determine the largest number that can appear in a 6×6 interesting board.
b) Prove that there is no interesting board of dimensions 7×7.
boardcombinatoricsnumbers