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

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.