## Nov 15, 2009

### 5 cards magic trick

Two magicians, John and Hull, perform a trick with a shuffled deck of cards, jokers removed.  John asks a member of the audience to select five cards at random from the deck.  The audience member passes the five cards to john, who examines them, and hands one back.  John then arranges the remaining four cards in some way and places them face down, in a neat pile.
Hull, who has not witnessed these proceedings, then enters the room, looks at the four cards, and determines the missing fifth card, held by the audience member.  How is this trick done?

Note: The only communication between John and Hull is via the arrangement of the four cards.  There is no encoded speech or hand signals or ESP, no bent or marked cards, no clue in the orientation of the pile of four cards...

1. First of all, we give numbers to all the 52 cards, so that no two cards have the same number.
For example- Clubs Ace- King have numbers 1-13, Diamond A-k 14-26, Hearts A-k 27-39, Spades A-K 40 -52.
Now, there are five cards and only four suites, so there will be at-least one suite which has two cards in the five randomly selected cards. John gives the audience member one of the cards of the suite which has more than one cards. He keeps the other card as the first card, through which Hull will be able to tell the suite of the given card.

We now need to decide the number of the card given. For this assume the cards to be circular.
For Example- the difference between K and A is 1, and the difference between A and 2 is also 1.

We also know, that no two cards have a difference greater than 6 either clockwise or anti-clockwise.

Now, we have 3 cards left, which have distinct numbers attached to them. without loss of generality, let us assume they are 1,2,3. These cards can be arranged in 6 ways (1,2,3 1,3,2 etc.). Each permutation will represent a number from 1 to 6 (ex- 1,2,3 = 1 & 1,3,2 = 2 etc. ) and the first card will be set as the reference card. The card given to the audience will be in the clockwise difference less than 6 to the reference card (ex- if there are A and K of the same suite, the user will be given A, K will be reference and the permutation of the remaining cards will give the difference as 1).

This way Hull will be able to say which is the card that the audience member has.

2. how can u make assumption of rest 3 cards will have different numbers attached ti them. they could be same...

3. No, the numbers are from 1 to 52, not not 1 to K.

4. AnonymousMay 30, 2015

If K is reference card and the taken off card is 7 ?

5. then take 7 as reference instead