MathDB

1

Part of 2023 Turkey Junior National Olympiad

Problems(1)

Boxes and Balls

Source: 2023 Turkey Junior National Olympiad P1

12/22/2023
Initially, there are nn red boxes numbered with the numbers 1,2,…,n1,2,\dots ,n and nn white boxes numbered with the numbers 1,2,…,n1,2,\dots ,n on the table. At every move, we choose 22 different colored boxes and put a ball on each of them. After some moves, every pair of the same numbered boxes has the property of either the number of balls from the red one is 66 more than the number of balls from the white one or the number of balls from the white one is 1616 more than the number of balls from the red one. With that given information find all possible values of nn
combinatorics