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'The Best Card Trick?' printed from http://nrich.maths.org/

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In the video below, you can see Alison and Charlie performing a card trick for Yanqing:
 
Can you figure out how Alison and Charlie's code works?
 
The video below shows two more examples of the trick; do these examples confirm your initial ideas about the code?
 

 

This crib sheet fell out of Charlie's pocket after he had performed the trick.
Can you use it to make sense of the code?
 
Find someone to work with, and together practise the trick until you can impress someone with your mathemagical skills!
 
Alternatively, if you are working on your own, here are sets of five cards that might be handed to you:
9H, 6D, 5C, 4D, 10S
2C, 10S, 3H, QH, 8D
KH, 7D, 7H, 7C, 7S
 
For each set, work out which four cards you would show, and in which order, so that a partner could work out the fifth card.
 
Notes and Background

This trick first appears in Wallace Lee's book "Math Miracles" in which he credits its invention to William Fitch Cheney, Jr., a.k.a. "Fitch."

You can read an article by Michael Kleber, the first part of which describes the trick, here.