IMO Shortlist 2013 problem C8

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Dodao/la: arhiva
21. rujna 2014.
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 1/2^m units of ink from the pot. Player B then picks an integer k and blackens the interval from k/2^m to (k+1)/2^m (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 [0, 1] is not completely blackened.

Decide whether there exists a strategy for player A to win in a finite number of moves.
Izvor: Austria