On a board there are written the integers from 1 to 119
Source: Moldova TST 2021
September 20, 2021
combinatoricsCombinatorial gamesgamecombinatorial game theorywinning strategy
Problem Statement
On a board there are written the integers from to . Two players, and , make a move by turn. A consists in erasing numbers from the board. The player after whose move two numbers remain on the board wins and his score is equal with the positive difference of the two remaining numbers. The player makes the first move. Find the highest integer , such that the player can be sure that his score is not smaller than .