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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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No Subject | Comment 43 of 51 |
  If magicians A uses a simple chart memorized ahead of time, all magician B would have to convey with his card is the position of the audience members chosen cards by their value relative to one another: greatest, second greatest, second least, and least.   For example, from left to right the cards chosen are 45, 34, 76, and 12.  Therefore, the combination would be: second greatest, second least, greatest, least.  Convert this sequence back into numbers 1-4 will get 3241.  There are only 24 4-number combinations of the numbers 1, 2, 3, and 4 if each number is used only once in each combination.  Magician B knows that 3241 is number 16 on the list, so he chooses card 16.  if that number has already been chosen by one of the audience members, the afallback would be to go from 100 and count backwards.  Done. 
  Posted by todd on 2007-09-18 21:19:19
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