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 Stage performance by brianjn)

Perhaps I should have made this D4.. The calculations that A has to perform, at least in the solution I came up with, aren't really easy enough to be just performed by "normal" human being's brain(i.e. I'm not able to solve everything in my head without paper in reasonable time without practice). These magicians however are considered to be mathematicians who are able to do such calculations in reasonable time. This problem is from Finnish high school math contest :)

Posted by atheron on 2007-05-12 07:20:00