Problem #WSP-000209

Problems Discrete Mathematics Algorithm Theory Game theory Winning and loosing positions

Problem

Fred and Johnny have a number $1000$ written on the board. In their turn, a player wipes out a number currently on the board and replaces it with either a number $1$ smaller, or half of the number on the board (rounded down). A player that writes $0$ on the board wins. Johnny starts, who will win?

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