Process of elimination is a great approach here, since as Economist
did above, you can quite quickly rule out wrong answers here. You can also see why 9 is the correct answer if you know one elementary fact from number theory:
-to find the remainder when you divide a number by 9, you can add the digits, and find the remainder of that sum.
Because we can find remainders when dividing by 9 by adding digits (and the same works for 3), the numbers ABCDE and EDCBA must have the same remainder when we divide them by 9. That is:
ABCDE = 9q + r
EDCBA = 9k + r
So ABCDE - EDCBA = 9q + r - (9k + r) = 9(q-k)
and their difference is a multiple of 9.
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