Originally posted by roygoh
OK. Here's some algebra:
For the 2-digit number that you pick, let "a" be the most significant digit and "b" be the least significant digit, thus 1<=a<=9 and 0<=b<=9.
"a" cannot be 0 or else it will not be a 2-digit number anymore.
Then the 2-digit number has a value of 10a + b
The sum of the 2 digits is a + b
Subtract the sum of the 2 digits from the original 2-digit number, and the result is (10a + b) - (a + b) = 9a.
Since "a" is an integer from 1 to 9, then the result is always a multiple of 9 (from 1x9=9 to 9x9=81), no matter which 2-digit number you pick at the beginning.
So, the trick is to assign the same symbol to all multiples of 9 from 9 to 81, and always show that symbol in the crystal ball. even though 90 and 99 are also multiples of 9, they will not be the results because the limit is 9x9 = 81. So the symbols for 90 and 99 can be different.
- Roy