The amazing Amber.

Amber has been amazing her friends with a math trick. Amber has a friend select a three-digit number and reverse the digits. The friend then finds the difference of the two numbers and reads the first two digits of the difference (from left to right). Amber can always tell the last digit of the difference. Explain how Amber does this.

Hint:

Let's say Amber's friend picks the number abc that is: a*100 + b*10 + c.

Reversing the digits will be cba that is c*100 + b * 10 +a

The difference of the two numbers is xyz that is x*100 + y*10+z

Start with finding the difference of the two numbers abc-cba based on the above assumptions and set that equal xyz . That is:

xyz = abc-cba