Add arithmetic operators to make 3 1 3 6 = 8 true

Add arithmetic operators (plus, minus, times, divide) to make the following expression true: 3 1 3 6 = 8. You can use any parentheses you’d like.

My initial thoughts (Solution):
I look at the tail of the equation, i.e., the ‘6’ and its relation with the answer we try to hit, ‘8’. Well, you have have any of the following to make it true:

  1. 2 + 6 = 8. But I can’t think a way to make ‘3 1 3’ into ‘2’.
  2. 14 – 6 = 8. But with ‘3 1 3’, the largest number we can make is (3+1)*3 = 12.
  3. 48 / 6 = 8. Again you can’t get 48 with ‘3 1 3’.
  4. \frac{4}{3} * 6 = 8. Therefore we need 4 and 3. That’s easy. (3 + 1) / 3.

Hence the solution is (3+1)/3*6 = 8.

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3 Comments (+add yours?)

  1. kelsoking
    Jun 22, 2012 @ 22:58:55

    I believe another solution is: (3 + 1) / (3 / 6) = 4 / 0.5 = 8
    Cool that there are two solutions. Anymore?

    Reply

  2. ariadna
    Jun 18, 2013 @ 11:02:09

    3 + 1 + 3 + 6 >= 8

    Reply

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