If you've read NUMBERS - the Key to the Universe you'll already know what a strange number 9 is. There are lots of tricks you can do with it, but when the mm author Kjartan was visiting South Leeds High School, he was shown a fast version of one of the tricks by Sadikul Haque.
Here it is!
- Go and hide in a cupboard, or cover your eyes in some way so that you can't see what your friend is writing.
- Ask a friend to secretly write down ANY number (at least four digits long). e.g. 78341
- Ask the friend to add up the digits... e.g. 7+8+3+4+1 = 23
- ... and then subtract the answer from the first number.e.g. 78341 - 23 = 78318
- Your friend then crosses out ONE digit from the answer. (It can be any digit except a zero) e.g. 7x318
- Your friend then reads out what digits are left.e.g. 7-3-1-8
- Even though you haven't seen any numbers, you can say what the missing digit is! EIGHT
THE SECRET
This great trick relies on the power of 9.
- After your friend has added up the digits and subtracted them, the answer will ALWAYS divide by 9. If a number divides by nine, then when you add the digits up, they will also divide by 9. If you check our example 7+8+3+1+8 = 27 which does divide by nine.
- When your friend crosses a digit out, he then reads out the digits that are left. You add them up. In the example we had 7+3+1+8 = 19
- All you do now is see what you have to add on to your answer to get the next number that divides by nine! The next number to divide by 9 after 19 is 27. So you need to add on EIGHT. This is the number that was crossed out!
Here's another example:
Say the number written down is 873946284 (urk!).
Your friend adds the digits 8+7+3+9+4+6+2+8+4 = 51
Your friend does the subtraction: 873946284 - 51 = 873946233
(So far you have NO IDEA what numbers are whizzing around!)
Your friend crosses a digit out 87394x233 and tells you what's left.
You add 8+7+3+9+4+2+3+3 = 39.
The next number that divides by 9 after 39 is 45. As 45-39=6 this means that SIX is the missing digit!
Many thanks to Sadikul for showing us this, and also to his Dad for showing him!
Professor Fiendish's Tricks and Games
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