PUZZLE #49 Responses/hints

If you tried this mystery puzzle with an actual number or two you noticed that there were several things which always happened.

Of course if the number was a double digit like 11, then the difference is 0.

If not, then the last digit of the smaller number is always bigger than the last digit of the larger number. So the definition of subtraction tells us to borrow 10 from the first digit (note the similarity to Puzzle 48?). This means that if the larger number is ab, then we get the number with digits (a-1-b) (10+b-a) as the solution. But the sum of these digits is ?? and this tells us how to solve the problem.

For example, take the number 27 which has 72 as the reverse number. Then the difference is

72

-27

45

where 4 = (7-1-2) and 5 = (10+2-7). Now add the numbers together to get 9 (why is the sum always 9?).

This means that if I am given the 4 I know that the other number is 5 and I win!!!