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The Best Card Trick?

Age 11 to 16
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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