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Science School – A Maths Magic Trick

I’m going to show you how to use maths to do a magic trick.  You may not have noticed this, but there is a pattern in numbers whenever you multiply them by nine, and you may have seen this in the nine times table because if you go through every single answer in the nine times table and you add the digits together, they always give you nine.  So one nine is nine, OK that’s very straight forward, two nines are eighteen, and one plus eight gives you nine, three nines are twenty seven and two plus seven gives you nine, it goes all the way down, right through the whole table, right down to nine nines are eighty one, and eight plus one gives you nine.  

And this works with bigger numbers, in fact any number you multiply by nine, if you add all the digits together, you get another multiple of nine; you always get something else in the nine times table.

Now you can use this to do a trick.  So, what you do is you get someone to get a calculator so you can’t see it, you tell them you're going to read their mind.  Get them to type in any number that they want, multiply by nine and then get them to read out all of the digits apart from the last digit.  In your head you're going to work out what that last digit is and you can do this by adding together the digits as they call them out.

Let’s say for example they call out the digits and they say OK, I’ve got a one, a five, a two and a four and you think, OK, one, five, two and a four, one plus five is six, plus two is eight, plus four is twelve.  Now twelve isn't in the nine times table, what’s the next number in the nines times table?  It’s eighteen, and I have to add six to get from nine to eighteen and so you can pretend to read their mind and say, ah, the last digit will be a six.  And if you use that pattern, you can always do that trick, but practice first, multiply some numbers by nine and make sure if you add the digits, you always get another multiple of nine.