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 limitations by Charlie)

B doesn't need to encode all the P(100, 4) possibilities, just the 4! = 24 arrangements of the selected 4 cards, as Jer has observed.

But even if B can use some kind of modulo 24 clue, the cards are shuffled before A gets them. So how does A know which is B's card?

Also, since the problem doesn't specify that B hands the cards to A, the magicians can't use that ingenious extra bit depending on the orientation of the pack.

Hmmmmmm.

Posted by JayDeeKay on 2007-05-11 14:16:43