2n consecutive integers on a board, replace pairs by their difference and sum
Source: Tournament of Towns, Senior A-Level Paper, Spring 2020 , p6
June 3, 2020
consecutivenumber theorycombinatorics
Problem Statement
There are consecutive integers on a board. It is permitted to split them into pairs and simultaneously replace each pair by their difference (not necessarily positive) and their sum. Prove that it is impossible to obtain any consecutive integers again.Alexandr Gribalko