Recently when I chatted with Jeremy Fleischman, he gave me a challenge. I don't know where this challenge was originated, but it was definitely nontrivial.
I think many people have tried scrambling and solving the Rubik's cube using two generators: U and R. Now the challenge is a modified version of that:
Define X = R', F, R as a whole sequence. Then, scramble and solve the Rubik's cube only using X and U and their combinations. Naturally, you can do U2 and U', and also X2 = R',F2,R; and X' = R',F',R. But you can never just do R or F by itself.
It really took me a while to figure out some complicated algorithms. Good luck!!!