Spoiler alert: This post contains spoilers for Project Euler.
Problem 6
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
JS Solution 1 (brute force)
This one is easy enough to brute force (though that's not the only, or "best" way to solve)
JS Solution 2 (System of equations)
There's a neat solution in the overview attached the problem.
This isn't something I would have thought to come up with on my own. The overview pdf provides pseudo code, so I've translated that to JS.
Aside from the obvious lack of a need for any looping, the cool thing about this solution is that limit can be as high as your system/language can support.
Conclusion
It's pretty neat that the difference can be directly calculated with the 2nd solution. For fun, change the limit of both solutions to
Copy/pasteable: 10000000000
The first code block will most likely timeout, while the second one will complete instantly.