MathDB
Game with powers of 4

Source: 2020 1st OMpD L2 P2 - Brazil - Olimpíada Matemáticos por Diversão

July 8, 2023
combinatoricsPerfect Powersgame strategyGame Theory

Problem Statement

A pile of 20202020 stones is given. Arnaldo and Bernaldo play the following game: In each move, it is allowed to remove 1,4,16,64,...1, 4, 16, 64, ... (any power of 44) stones from the pile. They make their moves alternately, and the player who can no longer play loses. If Arnaldo is the first to play, who has the winning strategy?