MathDB

5

Part of 2019 China National Olympiad

Problems(1)

Operation on n by n grid with integers

Source: China Mathematical Olympiad 2019 Q5

11/15/2018
Given is an n×nn\times n board, with an integer written in each grid. For each move, I can choose any grid, and add 11 to all 2n−12n-1 numbers in its row and column. Find the largest N(n)N(n), such that for any initial choice of integers, I can make a finite number of moves so that there are at least N(n)N(n) even numbers on the board.
combinatorics