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6 November, 12:26

The difference between a two-digit number and that number reversed is 18. What could that number be? List all possibilities.

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  1. 6 November, 12:45
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    A two digit number can be written like AB or 10*A + B (for example the number 36 can be written like 3*10 + 6 = 36)

    You can write this problem as

    10*A + B - (10*B + A) = 18

    10*A + B - 10*B - A = 18

    9*A - 9*B = 18

    9 (A - B) = 18

    A - B = 2

    A and B are digits, that means that both are either 0,1,2,3,4,5,6,7,8 or 9 (except that A cannot be 0 bcs the first digit in a two digit number cannot be 0)

    So the combinations are

    9 - 7 = 2

    8 - 6 = 2

    7 - 5 = 2

    6 - 4 = 2

    5 - 3 = 2

    4 - 2 = 2

    3 - 1 = 2

    2 - 0 = 2

    And we have the numbers:

    97 (B is 79)

    86 (B is 68)

    75 (B is 57)

    64 (B is 46)

    53 (B is 35)

    42 (B is 24)

    31 (B is 13)

    20 (B is 2)
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