Two magicians A and B perform the following trick:

A leaves the room and B chooses 4 members from the audience at random. Each member chooses a card numbered from 1 to 100 (each chooses a different card) and after B has seen their cards he chooses a card from the remaining deck of cards. The 5 chosen cards are shuffled by an audience member and handed to A who just returned to the room. Prove that A is able to figure out which cards each member picked. Consider that the chosen members form a row and e.g. the leftmost member picks the first card and the rightmost member (B) picks the last card.

The cards that the 4 members of the audience have chosen form a some permutation:  EX: 41 25 88 36

With any set of 4 numbers, there are 24 specific arrangements. 

If the arrangement is viewed as a single large number (example:41 25 88 36 =  41258836)
, the second magician can clue the first magician to what exact arrangement has been chosen. This can accomplished by the second magician choosing a remaining number that cooresponds to the relative magnitude of the arrangement.  

For example:  41 25 88 36  can be interpreted as the 11th largest arrangement.  This can be represented by the second magician picking the number 11 as the fifth card.

It might take a little practice, but in time it should become easy to code and determine the arrangement.

This reminds me a lot of fitch's trick.





 

Posted by John zadeh on 2007-06-26 20:52:27