Here’s a number puzzle that’s bound to make your friends think you are either a mind reader or a magician.
Ask your friends to write down any two different numbers from 1 through 9 without letting you see them. Now tell them to reverse the two numbers. They now have two, two-digit numbers. Tell them to subtract the smaller number from the larger one.
Now they should take the number that resulted from the subtraction, reverse the digits, and add that number to the one they got when they subtracted. When they are finished, without looking at their notes you can tell them the answer is 99. They can do this with any combination of numbers with two different digits from 1 through 9, and you will always be able to tell them the answer, because it will always be 99.
Anytime this five-step process is followed with two-digit numbers from 1 to 9, the result will be 99. For example, suppose you choose 8 and 6 as your two digits. Eighty-six reversed is 68; 86 minus 68 is 18; 18 reversed is 81; and 81 plus 18 is 99.
86 Reverse 86 to make:
68 Subtract the smaller from the larger
18 Reverse these digits of the difference to make:
81 Add this to the previous number
Let’s try it with different numbers.
37 Reverse 37 to make:
73 Subtract the smaller from the larger
36 Reverse these digits to make:
63 Add this to the previous number
You can be even more impressive by using 3-digit numbers.
With 3-digit numbers the answer is always 1089. For example:
721 Reverse 721 to make:
127 Subtract the smaller from the larger
594 Reverse these digits to make:
495 Add this to the previous number
Incidentally, a practical application of this phenomenon is that if your checkbook doesn’t balance, and the difference between your balance and the bank’s is evenly divisible by nine, there are probably two transposed numbers somewhere.