Five Card Trick


A mathemagician asks a volunteer to give him five cards drawn from a pack of fifty-two. He hands one card back to the volunteer and arranges the remaining four in some sequence he chooses. He then hands the sequence to a second volunteer and leaves the room. His assistant enters. The assistant asks the second volunteer to read out aloud the sequence handed to him. The assistant ponders a little and correctly announces the identity of the card held by the first volunteer. How could this be done? In general, how large a deck of cards can be handled if n cards are drawn initially?


Do not remember.


  1. Five Card Trick by Colm Mulcahy in MAA Horizons, 10 February 2003.
  2. Interesting variations of the puzzle are in Card Colm by Colm Mulcahy in MAA Horizons, Feb 2005.
  3. Check out N-Card Tricks by Hang Chen and Curtis Cooper, The College Mathematics Journal, Volume 40, Number 3, May 2009 , pp. 196-203(8).
  4. A related puzzle at MathOverflow.Net.

Previous Puzzle: Find the Angle

triangle-puzzle Find the measure of angle "a" in the diagram.

Next Puzzle: Sum and Product

P is told the product of two integers chosen from [2, 99] and S is told the sum. The following dialogue ensues: (1) P says, "I do not know the two integers." (2) S replies, "I knew that already." (3) P exclaims, "Ah! I now know the two numbers.", (4) S smugly replies, "Now I know them too." What are the two numbers?

17 Aug 2011
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