Algebra-cadabra! Here’s a classic magic trick, and the mathematical secret behind it

Alex Bellos in The Guardian:

Playing-cards-007Irishman Colm Mulcahy is a legendary cardsmith in the mathe-magical community, and his lovely new book Mathematical Card Magic is jammed with entertaining and thought-provoking tricks.

Here's one that's in the book.

The good thing about this trick is that you need an attractive assistant, which is one of the best things about being a magician.

Okay, the assistant doesn't need to be attractive. But I like to aim high, and will assume that she is for the remainder of this post.

The trick was invented by William Fitch Cheney Jr, a US mathematics professor, in 1951. It was originally called Telephone Stud since it could be done over the phone. Mulcahy calls it Fitch Cheney's Five-Card Twist.

First the magician leaves the room, leaving the attractive assistant with the audience. She gives a full deck of cards to an audience member, and asks him or her to shuffle it and then to choose any five cards.

The assistant takes the cards, looks at them, places one face down, and places the four others face up and side by side.

The magician is allowed back in. He glances at the table and – abracadabra – names the hidden card. The audience gasps in awe, since there was no way he knew which cards had been chosen.

So how did he do it?

More here. [Thanks to Jennifer Oullette.]