## Tuesday, 22nd March, 2016

# Weird Arithmetic

Even in the age of the computer and its old-fashioned relative, the calculator, some quirks of arithmetic are just too good to miss (to ludamus, at any rate).

Ask a friend to name their favourite digit between 1 and 9: they may say, for instance, “6”.

Now give them the number 12345679 (that’s right – with the digit 8 missing), and tell the to multiply it by 54 (which is just 6 times 9). They can do it on a calculator, or if they’re the kind of person who likes cold showers every morning and goes about wearing a hair shirt, they can try it by hand with pencil and paper.

The answer will be 666666666.

Whatever digit they give you, just ask them to multiply 12345679 by that digit times 9: for instance, if they tell you that their favourite digit is 7, tell them to multiply by 63, which will give them 777777777, and so on.

It may be a pointless mathematical fact, or there may be a reason behind why it works which you might like to investigate. In any case, it’s fun and surprising.