We have a normal deck of 52 cards. We want to do the following magic trick:

A person from the audience chooses 5 random cards. The magician's assistant looks at the 5 cards, chooses 4 of them, hands them to the magician one by one face up and keeps the other one hidden. The magician then guesses the fifth card (the one that the assistant kept hidden) just by looking at the 4 cards he was handed in.

Is it possible to devise a strategy, so that no matter what the original 5 cards were, the trick always works?

I would just like to point out that the problem states that the assistant "hands them to the magician one by one FACE UP." So solutions with the card facing down is not only a bit of a giveaway that something fishy is going on, but doesn't satisfy the problem statement either.

Later!

Posted by nikki on 2003-06-03 12:39:39