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# All Change: the prediction

## I think you are thinking of the number ...9

# What's going on?

How is this possible? The answer is...

**psychology:** adding up loose change is an
everyday situation and because of that most people don't notice that subtracting the number
of coins in the hand removes all the 1 pences and turns all the 10 pences into 9
pences. It's a sort of thinking error buried in the puzzle.

**...and Maths:** 9 is a number with special properties, the sum of the digits in a 'nine product'
always totals nine. We have here as you always end up with n times 9 pences, where
the number that n stands for depends on the
number of coins you choose at the beginning)

# Celebrity Tricks:

Carol Vorderman recently admitted to using this 'nine product' trick when she does her 'mental magic' in the numbers round on TV show Countdown, but she uses the trick backwards. Add the digits in any number, then add the digits of the result and so on until you eventually come to a final single digit. If this is a nine then the original number is also divisible by nine. This works even if the original number was massive.

So, for example, the number 1737 is divisible by nine, since the sum of its digits is (1+7+3+7)= 18, and the sum of these digits (1+8)= 9.