I saw a puzzle like this once. In the days before radio, the commanders of army A and army B want to attack the enemy from opposite directions. Either would lose if attacking alone so neither will attack unless he knows that the other will also attack. So A gets into position and sends a carrier pigeon to B saying he's ready. B receives the message and confirms by pigeon to A that he's also ready. But now B realizes that A won't attack unless he gets the pigeon from B and B is unwilling to attack unless he knows this. A could send another pigeon to B but now A won't know if B got it, so now A is unwilling to attack. No matter how many pigeons are sent back and forth, there's no way each commander can know that the other will attack. The attack can't take place under these conditions.

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