arXiv I’ve previously written about the Namer-Claimer game. I can now prove that the length of the game is with optimal play from each side, matching the greedy lower bound. The upper bound makes use of randomness, but in a very controlled way. Analysing a truly random strategy still seems like it will be very …

# Tag: game

## The Namer-Claimer game

Consider the following game played on the integers from to . In each round Namer names a forbidden distance , then Claimer claims a subset of that does not contain any two integers at distance . After finitely many rounds, Claimer will have claimed sets that cover the whole of , at which point the …