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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)

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re(2): A Little Hocus Pocus | Comment 29 of 51 |
(In reply to re: A Little Hocus Pocus by Charlie)

100 cards. Although it could be adapted for more.

The method I was taught (and used) involved - "A little hocus pocus" i.e. a trick. to get part of the answer.

When I was taught it was explained that a complicated method was needed to determine the numbers but that "the trick" made those "almost impossible mental calculations" unnecessary. This complicated method was not given to me.

Based on that information and the problem being from an exam paper I assumed the existance of a complicated solution.

Apologies if I confused. I eagerly await the official solution.

  Posted by Vernon Lewis on 2007-05-13 18:02:02

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