Answer 1

Here are some of the trickiest problems:
https://en.wikipedia.org/wiki/List_of_NP-complete_problems

Solve any of those in polynomial time or prove that it is impossible.

I can't think of a problem more tricky than something computer scientists have been struggling with for decades and never solved.

If you do either of the above and share your results so other computer scientists agree you've completed one of the above, you'll get the computer science equivalent to the Nobel Prize and will be extremely famous. You'd probably have enough money to retire immediately too.

Solving any of the above in polynomial time will indirectly solve all the NP-complete problems in polynomial time because they have known polynomial time algorithms to translate between each other.

If that's more tricky than you really want, you could try the "Hard" problem solving questions on hackerrank.com I find some of them difficult. Hackerrank problems are generally a lot harder than challenges on sololearn.