no of 0's on the table is odd then max odd number on table is perfect square
Source: 2018 Saudi Arabia IMO TST I p2
July 28, 2020
number theorycombinatoricsPerfect Square
Problem Statement
Let be an even positive integer. We fill in a number on each cell of a rectangle table of columns and multiple rows as following:
i. Each row is assigned to some positive integer and its cells are filled by or (in any order);
ii. The sum of all numbers in each row is .
Note that we cannot add any more row to the table such that the conditions (i) and (ii) still hold.
Prove that if the number of ’s on the table is odd then the maximum odd number on the table is a perfect square.