# Mystic Maths

Think of a two digit number,*

Reverse the digits to get another two digit number,

Subtract the smaller two digit number from the other,

(* The two digits must be different)

9

How did I know?

## A Mathematics Lesson Starter Of The Day

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Topics: Starter | Algebra | Place Value | Puzzles

• Tom, Birmingham
•
• 75-57?

I think the answer will be a multiple of 9?
• Paul, Coventry
•
• Yes, and when you add the digits of a two digit multiple of 9 the answer is always 9
• JM, Ysgol Friars
•
• AB - BA = (Ax10+B)-(Bx10+A) = 9A-9B = 9(A-B)
• CF, Lancshire
•
• This is a great starter it is a quick way to see who can subtract without a calculator and it is a good way to demonstrate the use of algebra to generalise and prove things.
• Amy, Carlow Ireland
•
• 65-56=09 0+9=9 cool it really works.
• Amy, Carlow Ireland
•
• 65-56=09 0+9=9 cool it really works.
• Beth Lyons And Caitlin York, Us
•
• It is easy to find out how he did it all he did is sort numbers out from high and low.
• Gianni, Milan
•
• 52-25=27!
Not every number is like that!
• Miss Hughes, London
•
• My Year 4 class worked out that by reversing the numbers it always came to a multiple of 9. I was able to spot the pattern that when you use consecutive numbers (45, 56, 67, 78, 89) the answer will always be 09, as the lower tens digit will become the units and you will always have to borrow. Can anyone help me explain why ANY number, even a prime number, will result in a multiple of 9?
• Year 4, St Alban's Warrington
•
• Our Year 4 class found this interesting. Some found it hard and some found it easy. It is a good starter for the day.
•
• Declan one of my KS4 students used 99, which does not work.
• P6/5, Balfron Primary
•
• We enjoyed this challenge but still aren't sure why the answer is always 9!
• Mr Jones, UK
•
• If the digits are x and y then one number is 10x+y and the other is 10y+x.
When you subtract the 2 numbers you are left with 9x-9y which factorises to 9(x-y) and as x-y is greater than zero as the digits are not equal and you have subtracted the smaller number, the solution will always be a multiple of 9.
• Mr Hulbert, Kellett School HK
•
• Great starter for my Y6 class!
We asked if three different digits would make a certain number?
So far it has always been 18 ...
Four digit numbers?
• Mr Marshall, Denmark
• Monday, January 27, 2020
• My year 6 class enjoyed this starter.

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