The Jailer’s Dilemma | Solution
Picture the three men in a row. Let’s label them A, B, and C, with B being the guy in the middle (facing A, with his back to C).
Now, first off, C can see both A and B. If A and B have the same hat color (e.g., red), then he will know his hat color is different (e.g., blue). If they don’t, then he will stay silent because he doesn’t know.
Now, B can see the color of A’s hat. It will be red or blue. B also knows that C, behind him, can see both their hat colors. He will assume if C says nothing, then his (B’s) hat color can’t be the same as A’s. So whatever color A is wearing (e.g., red), then his must be the other color (e.g., blue).
A can’t see anything since he’s facing the wall, so both B and C would assume he would be silent.
What about the guy in the other room?
That’s unimportant. It’s just a sleight of hand. What this problem illustrates is how the key to the solution is always to first consider the simplest possibility.
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