A Mathematics Trick

My son received a magic box recently as a present. There are some nice tricks in it (disappearing coins and silks, etc.) but one mind-reading trick in particular caught my eye. First, a member of the audience choses a number from a set of cards, second the magician is then given minimal information about the number. The magician then works out the number chosen. Watch the following video for a much better explanation and to see the trick in action:

How does it work?

This mathemagician won’t reveal the secret of her trick but if you work through the following I’ll let you in on it! You can then work out WHY this works which is a far more interesting question.

Here are the 6 cards.

Try the trick yourself

• Choose a number from one of the cards.
• Now look to see if your number is present on any of the other cards.
• Show all the cards on which the number exists.
• The magician now quickly looks to the top left corner of every card that has been selected.
• S/he quickly adds all these numbers up.
• This total gives the number that has been selected!

How does it work?

Here’s the really interesting question about this trick since, of course, it has nothing to do with mind reading, but a useful property of numbers. Useful, since the binary counting system relies upon it. In the video the numbers of the top left hand corner of the cards are 1, 2 & 8 (1+2+8 = 11). On close inspection of the six cards you will notice that the numbers in the top left hand corners are 1, 2, 4, 8, 16 and 32. You will also notice that these six numbers do not appear on any of the other cards. So if you were to pick 16 as your secret number you would only show this card. Your challenge now is to try and work out why this works and, in particular why these particular numbers (1, 2, 4, 8, 16 and 32) are so important for the trick to work.

Clue

Click on the eye to reveal a clue. If you need a clue I suggested that you try to find out about binary numbers and how we convert binary (or base 2) into our decimal system (base 10). For example 11 would be written as 1011 in binary.

More Mathematics Tricks

There exist lots of other tricks like this. Andrew Jeffrey performs magic shows based on mathematics. I was lucky enough to ‘participate’ in one of his shows in Lisbon a few years ago. He has put together an e-book of mathemagical tricks and will send it to you for free if you sign up to his newsletter. All the tricks are based on mathematics and trying to work out why they work can be the basis for some rich mathematical work! Now where did I leave that rabbit?