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How do you make $21$ from the numbers $1$, $5$, $6$, and $7$?

  • You can use the operations of addition, subtraction, multiplication and division, as well as brackets.
  • You must use each number exactly once.
  • You cannot juxtapose numbers (i.e., 1 and 5 cannot be used as 15).
Gamow
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Colonel Panic
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    I would answer, but I found this link from another site that asks the same question. – Andrea Gottardi Nov 06 '14 at 15:59
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    http://meta.puzzling.stackexchange.com/questions/1348/a-policy-on-plagiarism?cb=1 – nicael Nov 06 '14 at 16:00
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    I thought the issue was with copying copyrighted material verbatim, without permission or attribution. I don't see plagiarism here. – frodoskywalker Nov 06 '14 at 16:07
  • I agree with @frodoskywalker - the premise of the puzzle is the same, but that doesn't mean the puzzle itself is plagiarised. We're not deleting all the Monty Hall, Green-Eyed Oracle and similar questions, after all – Joe Nov 06 '14 at 16:10
  • Yes, this is not plagiarism, but I think this question has to be deleted because you can easily answer it simply searching on Google. – Andrea Gottardi Nov 06 '14 at 16:11
  • I don't think that can be a criterion for deletion, I agree in spirit that we should not just be a dump of other sites, but what if someone comes up with a different answer – skv Nov 06 '14 at 16:15
  • I don't think another answer can be find, with this four numbers.. – Andrea Gottardi Nov 06 '14 at 16:16
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    I am not talking specifically about this question, but the very fact that googling gives you answers cannot be a criterion for deletion is my contention – skv Nov 06 '14 at 16:17
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    If being able to Google a puzzle is reason for deletion, then probably the vast majority of questions on this site would have to be deleted. – pacoverflow Nov 06 '14 at 16:27
  • Maybe I was too strict saying it has to be deleted, but If this question was mine, I would like to award someone who has really spent effort in finding a solution, and not who simply searched for it. – Andrea Gottardi Nov 06 '14 at 16:28
  • It seems there's a bit of confusion about what plagiarism actually is. To be clear: plagiarism is a verbatim copy from another source without attribution. If you flag as plagiarism and have found a source, for reproducibility, please include the link in your "other" flag. Thanks! –  Nov 06 '14 at 17:47

3 Answers3

16

If this is an acceptable question, here is the answer:

$$\frac{6}{1-\frac{5}{7}}=21$$

This is a pretty well known problem that, while the math obviously works, is unintuitive enough that it is sometimes difficult to solve the first time you see it.

kaine
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5

I came across this question a long time ago and after struggling with it came up with this:

$ \binom {6 + 1}{7 - 5}$

which is

$\frac {7!}{2!5!}= \frac {7 \times 6}{2} = 21$

JMP
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Paul Palmpje
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5

Observe

$1 = \frac{5}{7} + \frac{6}{21}$

and rearrange.

Colonel Panic
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