• The best way to look at how this works is to assign the digits of the number to variables and solve for what the solutions CAN be.

    Start by assigning the digits of the number a different variable.

    a = 5
    b = 4
    c = 3

    Then arrange them with powers of 10 that represent their place value. (ie. the 5 is in the hundreds position, 4 in the tens, and 3 in the ones)

    (100a + 10b + c)

    We then took this number and reversed it.

    (100c + 10b + a)

    We then subtracted those numbers.

    (100a + 10b + c) - (100c + 10b + a)

    By combining the like terms we get 99(a - c).

    We have now simplified the generic numbers but we need to see how many combinations this makes. Since the digits were decreasing, (a-c) is at least 2 and no greater than 8.

    When you make a list of all these combinations you get

    198, 297, 396, 495, 594, 693, 792, or 891.

    When any of these are added with their reverse you get 1089!!