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.

Considering the difficulty level set here, is the discussion more at a higher level, or has the author offered too low?

To be a valid stage performance (and Ady, I think, suggested he might be able to 'pull it off') the process needs to be quick and easy. 

There seems to be some heavy calculations needed for what I think I am observing.

Dej Mar?  I understand the cyclical idea.  Would you be somehow giving B a number which is 24*n away from, eg, the mean of the other 4 numbers?  A would have to be quick to determine that number, particularly if it 'wrapped' around 100. 

I could understand 24*1, 24*2, 24*4 and 24*4 could represent some coded info, but what?

Posted by brianjn on 2007-05-12 05:06:41