• A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute is it on or off?
• Your twin guards know the left door from your cell leads to freedom, the right door to death. You cannot tell the twins apart, but you know that one always lies, and one never does. What one question can you ask either guard to find out which door to open?
• The king decrees that truth-value of the condemned man's final statement determines his fate: true, he hangs; false, he's shot. What statement (that doesn't refer to itself) can let the condemned man avoid both fates?
  
• You pick one closed box of three on a game show. As is his policy, the host shows you that one of the other two was empty and asks if you want to switch to the third. Should you switch?
• $N is in one envelope, $2N is in the other. You pick one randomly, and then are offered the chance to switch to the other.  The expected value of the other envelope seems 25% higher (because (2N + N/2)/2 = 5N/4). Is it?
• The godfather's three wisest henchmen gathered around the table each know that at least one of them has had a mark placed on his forehead, but each can see only whether the others do. The first one to deduce whether he has a mark becomes consigliere; an incorrect deduction means death. At some point one confidently announces his status. What is it, and how did he know?