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"The players may not communicate in any way" - It seems to me that all the answers are a form of communication. In fact the dictionary defines communicate as, "share or exchange information."

What a joke: "find a strategy for the players to determine the colours of their hats based on the hats they see and what the other players do"

I interpreted it in the same way as you did - communication on any level is not allowed. If there is no sharing of information then I think it is impossible to solve the puzzle.

It is possible without communication (also without seeing what the other players do).

How so?

Some answers have been posted already.

To me it looks like a mix between the Prisoner's Dilemma (https://en.wikipedia.org/wiki/Prisoner%27s_dilemma) and Blind man's bluff poker (AKA Indian Poker) https://en.wikipedia.org/wiki/Blind_man%27s_bluff_(poker)

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