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Hard · Market Microstructure · Quant Trader interview question · logic, probability, axiom-of-choice, game-theory
An infinite number of traders, numbered $1, 2, 3, ...$, are participating in a game. Each trader is wearing a hat that is either red or blue. Each trader can see the hats of all other traders, but not their own. Simultaneously, each trader must guess the color of their own hat. They win the game if only a finite number of traders guess incorrectly. Assuming the Axiom of Choice, can the traders devise a strategy to ensure that they win the game? If so, what's the core idea behind the strategy and