We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of several protocols with countably many prisoners.

中文翻译：

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具有多种颜色的各种协议的帽子拼图之间的战略对等

我们用无限多的囚犯和两种以上的帽子颜色来讨论“囚犯和帽子的谜题”。假设这组帽子颜色配备了可交换的群结构，我们证明了具有可数众多囚犯的几个协议的谜题之间的战略等效性。