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.

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.