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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(3): please read | Comment 27 of 51 |
(In reply to re(2): please read by Charlie)

I've found a small bug in the program, that does not affect either the first list of results (7/24 bad), or the percentages quoted in my previous post, but strictly speaking, the line

newNumb = ak + Z

should be followed by

if newNumb > chc then newNumb = newNumb - chc

I haven't worked out what fraction of the time this comes into play, but apparently it is small, as the percentages of incorrect are still the same to the nearest whole percent.


  Posted by Charlie on 2007-05-13 11:40:52
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