As for the second example, suppose we have the three digit number ABC with smaller reverse CBA. Since this is smaller, it must be that C < A. Subtracting the smaller from the larger gives us (A  C)0(C  A). Except C is less than A, so there must be a borrow for the last digit's subtraction: we actually get (A  C  1)9(10 + C  A). Finally, adding this to its reverse gives 9(9 + 9)9 = 1089.
Last edited by Indistinguishable; 08262016 at 04:01 AM.
