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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 11 to 119119. Two players, AA and BB, make a move by turn. A movemove consists in erasing 99 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 AA makes the first move. Find the highest integer kk, such that the player AA can be sure that his score is not smaller than kk.