## The Magic of Mathematics: Amaze Your Friends

Maths isn’t
always deadly serious. To prove it, here’s a card trick to
amaze your friends in the pub. It was invented by Arthur Benjamin,
a mathematician and magician at Harvey Mudd College in California.

Take a pack
of cards and deals the top 16 face down in four rows of four. Turn
four of these cards face up. Call for a volunteer from the audience,
who will repeatedly ‘fold up’ the square of cards, like
folding a sheet of stamps along the perforations, until it ends
up as a single pile of 16 cards.

The audience
will decide where the folds occur. For instance, the first fold
can be along any of the three horizontal lines between the cards,
or the three vertical lines.

When the cards
have been folded into one pile, the volunteer spreads them out on
the table. Either 12 cards are face down and 4 face up, or 4 cards
are face down and 12 face up. In the first case, the face-up cards
miraculously turn out to be the four aces. In the second case, the
volunteer takes the four face-down cards, and turnsthem over to
reveal… the four aces.

Magic!