In each round of the Namer-Claimer game, Namer names a distance d, then Claimer claims a subset of [n] that does not contain two points that differ by d. Claimer wins once they have claimed sets covering [n]. I show that the length of this game is of order log log n with optimal play from each side.

中文翻译：

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Namer-Claimer 游戏

在 Namer-Claimer 游戏的每一轮中，Namer 命名距离为 d，然后 Claimer 声明 [n] 的子集，其中不包含相差 d 的两个点。声称者在声称覆盖 [n] 的集合后获胜。我表明这个游戏的长度是 log log n 的顺序，每一方都有最佳游戏。