Silly Math

Alright, I've once again run out of standard "find the optimal strategy" type problems, its time for a seemingly simple math problem. I can't recall when I first learned this one, I've known it since at least grade 9:

Using the numbers 1, 5, 6, and 7, each once and only once, and +, -, x, and ÷ as much as you like, construct a formula for the number 21. You may also use as many brackets as you like.

To be clear, there are no stupid tricks in this problem, like sliding the 1 and 5 together to make 15. The solution is exactly of the form _*_*_*_, where _ is replaced by the numbers from {1,5,6,7} each used once, and * is replaced by {+,-,x,÷} (and can use repeats). You also have as many brackets as you need to control order of operations.

I always find this problem rather interesting because typically this sort of problem is either trivial or impossible, but this one is neither. There is a funny blind spot people tend to have with this.

Also, if you are in the mood, try using 3,3,8,8 to make 24 with the same rules. This one will be much easier after you have solved the first one.