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 please read by Charlie)

Absolutely correct.  This ends up being equivalent to saying that B's choice choice must tell A what the order of all 5 cards is.

Thus, to do this trick with 4 audience members requires at least cards 1 through 124, giving B 120 choices (enough to encode 5!).

If we plug into your analysis, right side is P(124,4) = 124!/120! = 124!/(119!*5!) = C(124,5) is left side.

So, the question now is do we have a method that works when there are 124 cards?

-- Joel

Posted by Joel on 2007-05-12 21:47:05