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2008 ToT Spring Senior A P2 game on the real line, strategy wanted

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March 7, 2020
game strategygamecombinatorics

Problem Statement

Alice and Brian are playing a game on the real line. To start the game, Alice places a checker on a number xx where 0<x<10 < x < 1. In each move, Brian chooses a positive number dd. Alice must move the checker to either x+dx + d or xāˆ’dx - d. If it lands on 00 or 11, Brian wins. Otherwise the game proceeds to the next move. For which values of xx does Brian have a strategy which allows him to win the game in a finite number of moves?
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