Explore BrainMass

three-digit number and reverse the digits

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.
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

Solution Preview

I wouldn't say there's a formula or a proper methodology for solving this kind of problems. It's a trick and it should be treated as such.
Just follow the hint:

The original number is a*100 + b*10 * c, where a, b, c are its digits. Just like 562 = 5*100 + 6*10 + 2 = 500 + 60 + 2
Now, in reverse order the number is c*100 + b*10 + a. For example, 562 in ...

Solution Summary

A case of a three-digit number and reversing the digits is brainstormed.