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Home > News > News Archive > Marvellous maths explained. The mystery of the number 1089.

Marvellous maths explained. The mystery of the number 1089.

1089 maths

In the last issue of Motor Technology News we ran a short article entitled Marvellous Maths, The Mystery of the Number 1089.

The mystery is this: first, take any three digit number, where the first and last digits differ by two or more and reverse the number to produce a new one. Then subtract the smaller from the larger producing another new number. If you reverse this number and this time add the two, the result will always be 1089.

For example, if we begin with 452, reversed we get 254, and taking the smaller from the larger, 452 – 254 = 198. If we reverse this number and then add the two we get 891 + 198 = 1089. And it always will be, regardless of the three digit number you start with.

To mathematicians of course there is no mystery and an explanation is given below.

Let us assume that the initial number is the larger and has digits a, b and c. So, when we reverse and subtract we will have (100a + 10b + c) – (100c + 10b + a)

This is the same as 100a +  10b + c – 100c – 10b – a = 99a – 99c = 99(a – c)

Because a and c are whole numbers, at the end of the first part of the process we will always end up with a multiple of 99.

The three digit multiples of 99 are: 198, 297, 396, 495, 594, 693, 792 and 891.

Now, note that the first and last digits of each number add up to 9.

So, when we reverse any of these numbers and add them together we get 9 lots of 100 from the first digit, 9 lots of 1 from the third and two lots of 90 from the second and so we get 900 + 9 + 180 = 1089.

No mystery at all really!