Magic Tricks based on deep Mathematics
mathoverflow.net
mathoverflow.net
"You, my friend, are about to witness the best card trick there is. Here, take this ordinary deck of cards, and draw a hand of five cards from it. Choose them deliberately or randomly, whichever you prefer -- but do not show them to me! Show them instead to my lovely assistant, who will now give me four of them, one at a time: the 7 of Spades, then the Queen of Hearts, the 8 of Clubs, the 3 of Diamonds. There is one card left in your hand, known only to you and my assistant. And the hidden card, my friend, is the King of Spades."
Here is a simpler one that impresses many people. Deal out 3 cards across, return to the top, 3 more cards, and so on until you've dealt out 27 cards in 3 columns. Have the other person pick a card but don't indicate what it is. Ask them to indicate which column has the card. Stack the 3 columns with that in the middle. Now redeal go through the same procedure. Repeat one more time. Now count the cards out. Card #14 is the picked card.
Why does it work? Well the first time you deal it could have been anywhere, the second time it is down to the 3 middle rows, the third time it is in the middle row, then you stacked it in the middle of the deck.
I think this was in one of the books by M. Gardner.