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Magic trick (Posted on 2007-05-11) Difficulty: 3 of 5
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.

No Solution Yet Submitted by atheron    
Rating: 4.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: please read | Comment 22 of 51 |
(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

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