How do you make 82 with the numbers

$4, 5, 6, 7, 8, 9, 0$

and 8 dots.

Get creative! You can use any mathematical operation, and the dots can be used in any mathematical way.

No ratios.

You must use every number.

Hint #1

The dots are to be used in an unexpected way.

Hint #2

How many ways can we use dots?

  • 1
    $\begingroup$ Isn't this just Sam Loyd's 1882 Columbus Problem? $\endgroup$ – royhowie Feb 20 '16 at 3:33
  • $\begingroup$ @royhowie Yes........ lol $\endgroup$ – bleh Feb 20 '16 at 4:03
  • $\begingroup$ @bleh you should probably add an notice saying that you edited it because you didn't factor in f's answer, otherwise you will get downvoted! Also the solution is readily available online. mathsisfun.com/puzzles/our-columbus-problem-solution.html I'd post this as an answer but people don't like linked answers XD $\endgroup$ – Daedric Feb 20 '16 at 12:28



$0.7$ to the zeroth power, multiplied by $98.4$ and $0.5$, is $49.2$. The ratio of this number to $0.6$ is $82$.

  • $\begingroup$ A and a +1 for effort. But more creativity than this. $\endgroup$ – bleh Feb 20 '16 at 0:18
  • 4
    $\begingroup$ @bleh, what do you mean? You know you don't get to say but that's not the answer I had in my head, try again!, right? If someone finds a solution to your riddle/puzzle, mark it as solved. Otherwise, we close it for being too broad. $\endgroup$ – user1717828 Feb 20 '16 at 0:47
  • 3
    $\begingroup$ @bleh If this solution violates something that your intended one doesn't (and "it's not creative enough" doesn't count), then you can edit the question or post a new version to make it narrower. $\endgroup$ – f'' Feb 20 '16 at 2:01
  • 2
    $\begingroup$ @bleh Also, if you do try to improve your question, I would suggest clarifying or specifying the part about "any mathematical operation", so that I can't say something like "$7409\ddot{:::}685$, where $\ddot{:::}$ is defined as the operation of taking the square root of the difference of two numbers". $\endgroup$ – f'' Feb 20 '16 at 2:05
  • 2
    $\begingroup$ This is totally acceptable, the OP is human, and was expecting x answer and didn't factor in the possibility of f's answer. You just need to make sure your don't do this too often. Threats of closing? Sounds like blackmail to me. $\endgroup$ – Daedric Feb 20 '16 at 12:24

That's easy, if we remember our SATs...

60 : 984 :: 5 : ?

Thanks, analogies!

  • 1
    $\begingroup$ You could also do this: $984\cdot5:60$ (The ratio of 984 times 5 to 60 is 82) $\endgroup$ – f'' Feb 20 '16 at 0:01
  • $\begingroup$ @f' but it needs 8 dots ........ $\endgroup$ – Daedric Feb 20 '16 at 0:05
  • $\begingroup$ What's the double colon mean again? $\endgroup$ – user1717828 Feb 20 '16 at 0:05
  • $\begingroup$ @Daedric If all 8 dots are required, I would think the $7$ would also have to be used. $\endgroup$ – f'' Feb 20 '16 at 0:06
  • $\begingroup$ X:Y::A:B means that "X is to Y as A is to B" - it's another way of writing a ratio, typically used for comparing words rather than numbers, as in "A leaf is to a finger as a tree is to a person". $\endgroup$ – Zerris Feb 20 '16 at 0:08

Ok, I'll write my desired answer.

$80 + .\dot{9}\dot{7} + .\dot{5} + .\dot{4}\dot{6}$

Which is basically...

$80 + 0.97979797... + 0.55555555... + 0.46464646...$

that adds up to...

$80 + 198/99$

Which finally equals to


  • 4
    $\begingroup$ Do you accept your own answer because it is more creative? IMHO, f" answer is way more creative. His answer didn't use extra mathematical symbols apart from the dots. And he uses the dots in 3 ways, while you only use it in only 2 ways. $\endgroup$ – wilson Feb 22 '16 at 4:16
  • $\begingroup$ -1 because you accepted your own answer. $\endgroup$ – EKons Jun 24 '16 at 14:20
  • $\begingroup$ It's acceptable to do that... $\endgroup$ – bleh Jun 24 '16 at 19:42

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