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Figure Five Frenzy challenge

August 2, 2007

I “died” on that game early on with the following numbers: 10 10 10 11 4 and the goal was 9. I finally solved it (offline, after running out of time), but that seemed like a pretty challenging set of cards, and there are still a few numbers I am having trouble making with that combination. Anyone want to play…

Of the numbers between 1 and 20, I can make (so far):

1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18

missing: 2, 8, 12, 19, 20

So… let me know if you can make more out of those.

The rules are to use only + – x and /.  Even though the game doesn’t allow it, let’s say unlimited numbers of parentheses.  No powers, roots, decimals, factorials.

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12 Comments leave one →
  1. August 3, 2007 12:36 am

    How about: 10 + 10 + 10 / (11 + 4)
    which is actually
    [10 + 10 + 10] / (11 + 4) = 2
    (since it doesn’t follow order of operations, right?

  2. August 3, 2007 12:44 am

    OK I’m back
    10 / 10 + 11 − 10 × 4
    which is actually
    [10 / 10 + 11 − 10] × 4 = 8

  3. August 3, 2007 8:15 am

    Nice ones, Darmok. I like how division got used in that first one. I could only think of 10 x 10 / 4.

  4. August 25, 2007 10:44 pm

    10(4 – ((10 + 11)/10))
    = 10(4 – 21/10)
    = 10(19/10)
    = 19

  5. August 25, 2007 11:02 pm

    Oh, very cool, JD. How did you ever think of that?

  6. August 25, 2007 11:15 pm

    There’s a hard twenty-four (know the game?) – 3, 3, 8, 8, and the only solution involves creating a mixed numbers and adding or subtracting a whole number to or from it, and then dividing or multiplying to lose the denominator. So I looked to see if the trick would work here.

    I’m glad, btw, that you asked, and puzzled that I actually had an answer. How did I think of that? Did you really expect an answer?

  7. August 25, 2007 11:33 pm

    I do know the game twenty-four (minimally). I’m going to have to see if I can figure that one out now. You’re not allowed to combine to make a two-digit number (like 83 in your example above) are you? It’s just +, -, x, / and all the parens you want, right?

    As to whether or not I expected an answer, well, I guess I’d say I was hoping you had one. Sometimes I can re-create some of the thought process when I come up with things like that. I’m glad this was one of those times for you. 🙂

  8. August 26, 2007 3:16 am

    Well, here. Using 3, 3, 8, 8 (usual rules) make 24.

  9. August 26, 2007 9:58 am

    Gosh, even with your hint this one is not exactly jumping out at me. 🙂 Are factorials and exponents allowed?

  10. August 26, 2007 10:08 am

    I don’t know if this is allowed, but how about this:

    \frac{8\times3!}{\sqrt[3]{8}}

  11. August 26, 2007 10:43 am

    Cool, but nope, just +, -, X, /.

  12. August 26, 2007 10:50 am

    OK, I got it:

    8/(3-(8/3))
    = 8/(1/3)
    = 8×3
    = 24

    btw, there’s a similar challenge over on the sidebar at

    Text Savvy

    I might have gotten that link from your blog actually, but in any case if anyone else is following this discussion, they might be interested. I had a lot of fun with that one.

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