Problem #WSP-000209

Problems Discrete Mathematics Algorithm Theory Game theory Winning and loosing positions

Problem

Fred and Johnny have the number \(1000\) written on a board. Players take turn to wipe out the number currently on the board and replace it with either a number \(1\) smaller, or half of the number on the board (rounded down). The player that writes \(0\) on the board wins. Johnny starts, who has the winning strategy?