MathDB
Game on the board

Source: Latvian TST 2021 Day P4

March 12, 2021
combinatorics

Problem Statement

Initially, on the board, all integers from 11 to 400400 are written. Two players play a game alternating their moves. In one move it is allowed to erase from the board any 3 integers, which form a triangle. The player, who can not perform a move loses. Who has a winning strategy?