Problem
First name
Aanya Goyal
School
Arnhem Wharf Primary School
Country
Age
10
Email address
goyalaanya82@gmail.com
Alison picks out a random three-digit number, which could be written as xyz.
The value of xyz is 100x+10y+z. Then she gets the reverse of xyz, the value of which is 100z+10y+x.
Subtracting 100z + 10y +x from 100x + 10y + z gives us 99x – 99z. If we call it A, then A is a multiple of 99 because (x-z) is an integer. So only possibilities for A are 099, 198, 297, 396, 495, 594, 693, 792, 891, and 990. B is reverse of A. So B is going to be 990, 891, 792, 693, 594, 495, 396, 297, 198, and 099.
Adding A and B together will always give us 1089 (099 + 990, 198 + 891, etc).
It will not work if x = z because then x - z = 0. Then A will be 0 and B will be 0.