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.

(In reply to a good start to go on ( no spoiler!!) by Ady TZIDON)

The numbers 1 through 100 should be thought of as circular...that is, after 100 follows 1,2,3 again.  This will provide another possible gap sequence of 24.  A duplicate length of possible gaps should be avoided when determining where the gap should begin.  B's number then should be able to be determined by where the gap of 24 is.  And, after determining what B's number is, the other four number can be ordered by the one of twenty-four possible arrangements that B's number indicates.   

Posted by Dej Mar on 2007-05-11 22:43:37