Year 12s: what will be the first way you research your future options? >>

Weird pattern

So I was just playing around with some numbers and realized every number goes back to 9 if you add it's digits and write that sum underneath and subtract.

An example to make it clearer:

start with 23 2+3=5 23-5=18 1+8=9

57 5+7=12 57-12=45 4+5=9 etc

Is there any reason for this... It just seems really bizarre.

Reply 1

brianeverit

Original post by maths learner

Consider the two digit number with digits a and b. Then the number may be written as 10a+b
Subtracting the sum of the digits we have 10a+b-(a+b)=9a
Can you complete it and see whether it works for any 3 digit number?