MMO 336 Moscow MO 1956 64 numbers with 1956 sum, square table
Source:
August 19, 2019
Sumcombinatoricsalgebra
Problem Statement
non-negative numbers whose sum equals are arranged in a square table, eight numbers in each row and each column. The sum of the numbers on the two longest diagonals is equal to . The numbers situated symmetrically with respect to any of the longest diagonals are equal. (a) Prove that the sum of numbers in any column is less than .(b) Prove that the sum of numbers in any row is less than .