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?
people are making this too difficult - you're not trying to determine a card from the entire deck, you're trying to determine the easiest of five cards from the deck.
So yes, the first card can surely nail the suit of the target card, as the assistant will chose a card that has a duplicate suit to be guessed (or for repeat showings, a certain suit could mean the target card is a certain other suit to more easily camoflage the method).
This leaves only 12 cards to choose from, which can be narrowed down easily enough with the three remaining cards, with a number of methods, some of which presented before me....
my solution
