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.

1. A and B are the same magician, although the audience believes they are two different magicians.  Not too difficult a trick for a good magician to perform.

2. A leaves the room and a half-second later B enters the room (but looks quite different from A).

3. B chooses 4 members from the audience at random, who each choose a different card.

4. B then picks his card.

5. An audience member then shuffles the cards.

6. This is when B leaves the room and a half-second later A returns to the room looking like he did before.

7. The audience member hands the shuffled cards to A, who already knows which member picked which card since he is also B.

Posted by Guest on 2007-05-15 19:47:28