Consider an integer n≥2 and write the numbers 1,2,…,n down on a board. A move consists in erasing any two numbers a and b, then writing down the numbers a+b and ∣a−b∣ on the board, and then removing repetitions (e.g., if the board contained the numbers 2,5,7,8, then one could choose the numbers a=5 and b=7, obtaining the board with numbers 2,8,12). For all integers n≥2, determine whether it is possible to be left with exactly two numbers on the board after a finite number of moves.Proposed by China RMM 2021combinatoricsboardRMM