This is a very nice puzzle that kept me awake for a long time... :-)
John and Dianne, two journalists (and experienced bridge players), are captured by some foreign government. The guardian says that he can free them, if they win the following game. First, Dianne must choose five random cards from a standard 52 card pack. Then, she must send one card at a time (through the guardian) to John. When John receives the fourth card, it must correctly guess the fifth card that Dianne still has. If he guesses correctly, they are both free. Otherwise, they will both stay in prison forever.
Can John and Dianne exit the prison in these conditions?
Assumptions:- Before the actual game, John and Dianne can talk together for one day and decide their playing strategy. But, after that, they cannot communicate in any way - they are now completely isolated forever (or, at least, until they get out from the prison). Also, they are completely isolated from the outer world (no cell phones) etc. The only method to communicate between them will be through the cards that Dianne sends to John. - The time interval between delivering the cards cannot be used as a method to communicate information. In fact, the guardian might randomly delay delivering the cards to John just to make sure that they are not using this trick to send additional information.- Dianne cannot alter the cards the she sends in any way to send additional information. In fact, after receiving a card from Dianne, the guardian might send to John another (almost identical) card of the same type, to make sure that she didn't use the card to send additional clues to John.