# How to make 21?

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).
• I would answer, but I found this link from another site that asks the same question. – Andrea Gottardi Nov 6 '14 at 15:59
• meta.puzzling.stackexchange.com/questions/1348/… – nicael Nov 6 '14 at 16:00
• I thought the issue was with copying copyrighted material verbatim, without permission or attribution. I don't see plagiarism here. – frodoskywalker Nov 6 '14 at 16:07
• 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 6 '14 at 16:17
• 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 6 '14 at 16:27

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.

Observe

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

and rearrange.

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

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