Five Card Trick
17 Aug 2011
Puzzle

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?

Source

Do not remember.

Solution

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.