Sample Problem

Number and Digit are playing a game. They count the next 1, 2 or 3 consecutive natural numbers at a time in turns, starting from 1. The person who counts to 42 is the winner. If Number wants to win the game and the game starts with him, what number (s) should he count first?


In this game, the winning positions are 42, 38, 34, 30, …, 2, by working backwards. Therefore to start Number should count to 2, i.e. count 1, 2.