Easy question

...but worth thinking about how you can get the answer quickly.  And how many different answers there are.



This comes from brilliant.org


Comments

  1. Rook5 October 2017 at 14:22

    There are 16 possible solutions:
    Assuming
    a x b = c
    I + j = k
    x - y = z

    You start of by finding that c can only equal 6 or 8 meaning a or b must equal 2.
    Since you can also conclude that either k or x must equal 9 you can arrive with 12 different equations.
    When k or x = 9
    1,8
    3,6
    4,5
    5,4
    6,3
    8,1

    We will ignore the last there as they are just the other way around.
    We can find out that there is no way to use 1,8 or 3,6 but is a way for 4,5.
    We also know that a can switch with b, I can switch with j and y can switch with z. This gives 8 possible rearrangements.

    Since x or k could equal 9 there is double 8 amount of solutions making it 16.

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