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)

In my reasoning I didn't know if it was appropriate to state there were P(100,5) = 9,034,502,400 possible sequences A must reply, or what I actually gave there, P(100,4) = 94,109,400, as the fifth is determined by the other four, by default.

Posted by Charlie on 2007-05-11 13:44:50