The hidden card
[I learned about this problem from Lyle Ramshaw. See also puzzles 19 and 20 on
the following large collection of
In this problem, you and a partner are to come up with a scheme for
communicating the value of a hidden card. The game is played as follows:
- Your partner is sent out of the room.
- A dealer hands you 5 cards from a standard 52 card deck.
- You look at the cards, and hand them back to the dealer, one by one, in
whatever order you choose.
- The dealer takes the first card that you hand her and places it, face up, in
a spot labeled "0"'. The next three cards that you hand her, she
places, similarly, in spots labeled "1", "2", and "3".
The last card that you hand her goes, face down, in a spot labeled "hidden".
(While you control the order of the cards, you have no control over their orientations,
sitting in their spots; so you can’t use orientation to transmit information to your
- Your partner enters the room, looks at the four face-up cards and the
spots in which they lie and, from that information (and your
previously-agreed-upon game plan), determines the suit and value of the
Question: What is the foolproof scheme that you and your partner settled on ahead of time?
As a follow-up question, consider the same problem but with a 124-card deck.