Ask HN: What kind of side-project can I build to play with algorithms?

I want to work on a webapp as a side-project. But what I want to play with is algorithms, Computer Science things. Input text A, output text B.

So, what real problems could I try to solve with "classic" algorithms and offer as a webapp? Or, which fields could I explore to do so?

I don't know if it makes sense what I'm saying. But what I mean is: problem P which some people have. This problem can be solved through classic, standard algorithms. I create a terminal program that solves it and then I just connect it to a dead simple web frontend.

Basically, as an amateur I'm more or less "good" at solving this kind of problems (the typical ones that you would see in a CS course), and would enjoy trying to apply them at real life.

Thanks a lot, excuse my English.