*You put a deck of cards in your pocket, and invite anyone in the audience to call out a number between 1 and 15. Then you reach into your pocket, you take out a set of cards whose sum is the number that was called! How can you perform this magic trick?*

The magic of Binary!

Amazing.

From Su, Francis E., et al. "Binary Card Trick." Mudd Math Fun Facts:

*Every number between 1 and 15 has a unique representation as a sum of some collection of the numbers 1, 2, 4, and 8*(the four powers of two represented by a nibble, i.e. four bits).

*Before the trick starts, pick an Ace, 2, 4, and 8 and put them on top of the deck, and then put the deck in your pocket. Then when a number between 1 and 15 is called out, take the binary decomposition of the number, and use that to determine which of the first four cards you will pull out.*

*No one needs to know that you never need to use the other cards!*

## 1 comment:

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