A riddle was posted in this mathoverflow question: http://mathoverflow.net/questions/85439/how-does-intuitionism-handle-this-riddle

A riddle: You and another person are kidnapped and knocked unconscious by a demented villain. When you wake up, you are told that some of you may have an ink dot on your forehead. You can see the other person's forehead but not your own. You must each privately guess as to the status of your forehead. At least one of you must be right, or you will both be killed. No talking or signaling is allowed; this also will result in death.

Now, if you survive this, you and the other person will be transported elsewhere, never to see each other again. You will never know what was on your own forehead.

The solution to this riddle relies on the fact that there are exactly four possibilities: You both have a dot, neither has a dot, you do and she doesn't, she does and you don't. I'll leave it to the reader to figure out the strategy.

Even with the hint, and assuming that the configuration of dots was chosen uniformly at random (which is not stated in the problem), I don't see how to do better than just randomly guessing whether or not I have a dot, with a 25% chance of death.

If I'm allowed to communicate in advance with the other prisoner and devise a strategy, we can guarantee freedom by e.g. one of us guessing what he sees, and the other guessing the opposite of what he sees. But communication is explicitly forbidden in the question.

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Yes, but I assume that's referring to the intuitionism angle of the question and not the riddle itself. (At least, there's nothing in the comments suggesting that the riddle is ill-posed, though of course that's a possibility.) – user7530 Jan 11 '12 at 21:08
This riddle has no solution. Voting to close. – TonyK Jan 12 '12 at 0:20
Problem has been resolved: the OP (on mathoverflow) admitted that he meant that you were allowed to strategize beforehand. (Before the dots were drawn? Before you were kidnapped? Who knows.) Which makes the problem trivial. – mjqxxxx Jan 12 '12 at 5:00
If you are allowed to formulate a strategy beforehand, one player should agree to guess the same as what he sees on the other's forehead, and the other should guess the opposite of what she sees on the other's forehead. Exactly one of the two people will be right no matter the combination. – Marconius Jul 5 '15 at 22:23