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Are there any equations that look very hard to solve at first (e.g. many involved parameters etc), but can be solved/reduced efficiently solved with a certain algorithm? I'd like to create some programming problems/puzzles - hence the question.

I had the following ideas:

Given some integer and an equation, find a solution. The idea is that the problem should quickly explode in a computationally large problem, but can be solved very efficiently with some algorithm/trick.

Can anyone suggest some problems that could fit here? Maybe some diophantine equation problem, or something similar?

n00b.exe
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    The Rubiks cube comes to mind – pancini Apr 15 '20 at 21:52
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    Why do you ask? Some context would be helpful. $1 = xm + yn$ where the variables are integers and $m$ and $n$ are given is a classical example. – Rob Arthan Apr 15 '20 at 21:53
  • Just trying to think of some interesting problems, that give you the wow-effect once you see the solution. @RobArthan I've recently seen a paper on the LLL algorithm, that is kinda falls into this category too. – n00b.exe Apr 15 '20 at 21:58
  • @RobArthan I updated my question, to make it a bit more clear :) – n00b.exe Apr 15 '20 at 22:54
  • Not sure how well this answers the question, but might be of interest: https://mathoverflow.net/q/244184/30186 – Wojowu Apr 15 '20 at 23:01
  • This seems like a candidate for the discouraged tag "big-list". You'll have to clarify the scope, but my example would be the solution to Nim – Mark S. Apr 15 '20 at 23:04

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