Math magic?

Question

I'm supposed to explain how the trick works, but I don't even know how to figure out the missing digits. Can I get some help in figuring out the digits?

Select any three-digit number whose first and third digits are different. Reverse the digits and find the difference between the two numbers. By knowing only the hundreds digits in the difference, explain how it is possible to determine the other two digits. Explain how the trick works.

Answer 1

321 - 123 = 198

625 - 526 = 99

931 - 139 = 792

OK, here is the pattern. The tens digit is always 9. The ones digit plus the hundreds digit is also 9.

Given any two numbers as defined, one will be larger than the other. The larger one will have a larger number in the hundreds place. The smaller one will have that number in the ones place. Therefore, when we subtract the ones digits, we will have to borrow from the digit in the tens place.

The tens digits are the same, but because we have to borrow one for the ones column, the top digit is now one lower. We will have to borrow from the hundreds. The tens digit in the answer will always be 9.

Take as an example abc - cba. If we break that down into the different places, we get.

. . a-1. . . 10 + b - 1. . . . .10 + c
- . c . . . . .b. . . . . . . . . . . . .a

The tens digit: 10 + b - 1 - b = 9

When we add the ones and hundreds digits we get:
(10 + c - a) + (a - 1 - c) = 10 - 1 = 9.

Answer 2

what she said