Answer
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Solution: The first chef to shout out is Chef 2.
Here’s why:
- Chef 1 can see the hats of Chef 2 and Chef 3. If they were both the same color (either black-black or white-white), Chef 1 could immediately determine that their own hat must be the opposite color. However, Chef 1 doesn’t shout, which means Chef 2 and Chef 3 must be wearing different colors.
- Since Chef 1 does not shout, Chef 2 realizes that he and Chef 3 must be wearing different-colored hats.
- Chef 2 can see Chef 3’s hat. Therefore:
- If Chef 3 is wearing a black hat, Chef 2 knows he must be wearing white.
- If Chef 3 is wearing a white hat, Chef 2 knows he must be wearing black.
- Hence, Chef 2 is the first to shout, as he can deduce his own hat color based on the fact that Chef 1 remained silent.
Solution: Chef 2 is the first to shout because he can deduce his own hat color from the silence of Chef 1 and the color of Chef 3’s hat.