IMO 2013 Shortlist C8
Players A and B play a paintful game on the real line. Player A has a pot of paint with four units of black ink. A quant...
Category: Combinatorics
Problem
Players A and B play a paintful game on the real line. Player A has a pot of paint with four units of black ink. A quantity p of this ink suffices to blacken a (closed) real interval of length p. In every round, player A picks some positive integer m and provides 1{2m units of ink from the pot. Player B then picks an integer k and blackens the interval from k{2m to pk ` 1q{2m (some parts of this interval may have been blackened before). The goal of player A is to reach a situation where the pot is empty and the interval r0,1s is not completely blackened. Decide whether there exists a strategy for player A to win in a finite number of moves. (Austria) 6 IMO 2013 Colombia