Question

Waneek picks a two-digit number, subtracts the tens digit and then subtracts the ones digit to get a new number.

For example if she had picked 37, she would get
37 - 3 - 7 = 27
so her new number would be 27.

How many different numbers can be formed using Waneek's process?

Answer 1

its 5

Answer 2

Let x be the 10s digit.
Let y be the 1s digit.
So any two digit number is represented by 10x + y.
Subtracting the 10s digit and then the 1s digit gives 10x + y - x - y = 9x
So resulting numbers are all multiples of 9, regardless of which 2 digit number we start with.
The lowest value x can be is 1, giving a result of 9.
The highest value x can be is 9, giving a result of 81.
Filling in the remaining multiples of 9, we have 9 numbers that can be formed from Waneek's process:
9,18, 27, 36, 45, 54, 63, 72, and 81.