A friend got me hooked on PE by pointing me to #208 many years back. Lovely problem, recommended fun time. I wonder if folks here have favorite problems they've worked on as well.
What's fascinating to me about this one, though, is its difficulty level, versus what the design team thought that level would be. Those levels are set automatically based on how quickly PE members manage to solve it, and this one took 32 weeks to hit 100 solvers, for a 95% difficulty. But problems are usually scheduled in batches of 6, one per week, with an expected difficulty cadence of Medium, Easy, Medium, Easy, Medium, Hard. And #589 was expected to be an _easy_ problem! I can actually see, having solved it, why the team thought it deserved its easy slot, but, wow, did things work out differently.
For a more general favorite, I really enjoy solving any of the impartial game problems. I'm not pointing out which those are - part of the fun is discovering that that's what you're looking at.