Abstract
We consider the Maker–Breaker positional game on the vertices of the n-dimensional hypercube {0,1}n with k-dimensional subcubes as winning sets. We describe a pairing strategy which allows Breaker to win if n is a power of 4 and k≥n/4+1. Our results also imply that for all n≥3 there is a Breaker's win pairing strategy if k≥⌊37n⌋+1.
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