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 re(2): How i would do it - How it works by Brian Smith)

I like the idea, Brian, but a couple of problems:

1) What if the audience chooses two or more cards of the same value (i.e.: a pair of 3's)? I suppose the numbering of the deck could be absolute, such as 1 of clubs = 1,
1 of diamonds = 2, 1 of hearts = 3 ...) this way if the 3h came before the 3d then he would know that to be high then low.

2) The magician would have to mentally remove the 4 cards he is given from his numbering system, so that each time he does the trick the some of the cards will have different values (so if the audience chose 3c, 7d, 10s, Kh then the 5h becomes 19-1=18, the Qc becomes 45-3=42, etc. (assuming Aces low for ease of computation)).

3) As you said, it would be a lot of mental math. While this works perfectly with pencil and paper and no audience, it becomes very difficult to do on stage as a magic effect. It runs the risk of either taking to much time to be effective, or worse, causes people to be suspicious of how the trick is really done.

Posted by Chris on 2003-05-08 11:44:01