There must be a logical reason, but darn if I know it.
Because all of the possible “right answer” number combinations have the same symbol associated with them.
10: 1+0=1; 10-1=9; Check the symbol for 9.
22: 2+2=4; 22-4=18; Check the symbol for 18.
35: 3+5=8; 35-8=27; Check the symbol for 27.
9, 18, 27 = All the same symbol.
Easy. Think of a two digit number, X. Now call the first digit A and the second digit B. so, 10A + B = X, right?
Now, if you follow the directions, you subtract the sum of the digits from the original number. So, 10A + B - (A+B) = 10 A - A + B - B, or 9A.
Therefore, no matter what 2-digit number you think of, the solution is always going to be 9 times the first digit.
Now look at the chart. Specifically, look at every number divisible by 9. They’re all the same symbol.
The answer to the equation will always be 9, 18, 27, 36, and so on as multiples of 9 up to 89. The symbols change every time, and the symbol found on the multiples of 9 is always going to be your answer.
Whoops, strike that. Most are multiples of 9, but not all.
I saw this a while ago. I think the resultant difference of any two-digit number minus the sum of its digits will always be a multiple of nine. There are nine symbols that cycle over and over, with the same symbol always representing the multiples of nine. So even before you choose the numbers, the symbol is determined by whatever symbol represents 9, 18, 27, etc.