PS2 or GC - Challenging game, physically AND mentally, or just mentally?

So I'm looking for a PS2 or GC game, (though I'd much rather it be on the ps2) that is very challenging in the mental and physical sense. Shadow of the Colossus was a good example of a game that required me to actually think about how I was going to accomplish killing each boss. Though peoples opinions of whats challenging will vary, hopefully that gives a general idea of what I mean. I'm pretty much open to any genre style except side scrolling old school 2D type games.

For me, if a game is not challenging, its not very fun xD

Any suggestions? :)

EDIT: I want to give a better idea of what I meant by hard... Hard as in... I can't figure out how to precede, and I almost want to grab for that strategy guide but I tell myself NO! I have to figure this out! I can do this! Not hard in the sense that my reflexes aren't fast enough, though it playing a role in the difficulty is important..

F-Zero GX, it's hard as hell and requires strategy before a race.

Pikman is a great suggestion but I've already beaten both of them. I played F-zero too, though I never finished the campaign, which I played on the normal difficulty way back when.

Have you tried assassins creed or Silent Hill Shatered memories? But they are mostly psychological!

Have you tried assassins creed or Silent Hill Shatered memories? But they are mostly psychological!

tartardk

F-Zero GX, it's hard as hell and requires strategy before a race.

sonic_spark

F-Zero GX was really the only racing game I liked, the tracks were just so awesome. It was very hard, but I want more games like it to come out.