Numbers on blackboard replaced by difference
Source: Tuymaada 2018 Junior League/Problem 6
July 20, 2018
combinatoricscombinatorics solvedinvariantParityblackboard
Problem Statement
The numbers are written on a blackboard. They are divided into pairs. Then each pair is wiped off the board and non-negative difference of its numbers is written on the board instead. numbers obtained in this way are divided into pairs and so on. One number remains on the blackboard after ten such operations. Determine all its possible values.Proposed by A. Golovanov