Think of a number (and don't forget it). Double it. Add six. Divide your answer by two. Now take away the number you first thought of. The number in your head is now... three!
Magic? Well, it is to an eight year old. Until you understand the basics of functions and algebra, the thought that a number can be predicted is a surprising one. And of course "magic" and "being surprised" are often the same thing. Pulling a rabbit out of a hat is magic because it goes against what we expect, and also because we can't explain how it has been done.
Let's look at another example of mathematical magic. This trick is going to make a number you choose appear six times (to get the best effect it helps if you have a calculator). Think of a number between 1 and 9. Now multiply it by 7, then by 3, next by 11, then by 37, and finally by 13.
If you haven't seen it before, the result will surprise you and make you smile. And even adults have been know to regard this as a magic trick (especially when it's dressed up with a bit of appropriate patter).
Like all tricks, it has a perfectly logical explanation. The numbers 3, 7, 11, 13 and 37 are the prime factors of 111,111. Why does it appear magical? Because we like pretty patterns, and our experience tells us that multiplying lots of familiar "boring" numbers doesn't normally produce something pretty. Incidentally, numbers that are made up entirely of ones are known by mathematicians as "repunits", and repunits have many interesting properties. For example, 1112=12321. Half of all repunits are exactly divisible by 11, and the other half when divided by 11 give a remainder of 1. (Actually that result is pretty obvious when you think about it.) Because of its everyday factors, I find the six digit repunit the most interesting one of all.
Maths and magic have been partners for a long time. Back in the days of Pythagoras, numbers were connected more with mysticism than with conjuring, but discoveries like the "3, 4, 5" triangle were enough to make people believe that some numbers must have magical powers. In the 19th century, Lewis Carroll (a.k.a. Charles Dodgson, a maths lecturer at Oxford) was fascinated by all sorts of tricks and puzzles to do with numbers, some of which magicians still use today. And in modern times, the maths populariser Martin Gardner is one of many mathematicians who are also practising conjurers.
All of these mathemagicians trade off the fact that you can usually predict precisely the outcome of doing something in mathematics, but only if you know the secret beforehand. And since so few people know the secrets of maths, it provides rich possibilities for mind-reading and other "miraculous" deeds. (original text by Rob Eastaway, 2001)
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