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?

(In reply to ideas by Jon)

Hmmm... Usually the standard deck of cards will be completely symmetric, so you will be limited to only 2 positional variations per card: vertical or horizontal. That will give you 16 possible combinations.

One more thought - because you are seeing 4 of the 52 cards in the deck, they are eliminated, and there are only 48 possibilities left for card #5.

Provided you agree on some scheme for enumerating the cards beforehand, your assistant would need to communicate a number between 1 and 48 to indicate what card #5 is.

Posted by levik on 2003-05-08 07:22:46