[snewman]

Why do you say these are problems that are already solved? Sure, they're often variations on existing themes, but the same is true for chess positions and, honestly, almost everything else in any field of human endeavor.

Agreed that the absolute upper tier of chess players have trained longer and harder than most or all IMO contestants. Though I do wonder which (top-tier chess or the IMO) draws on a larger talent pool. To my understanding, a significant fraction of all high school students on Earth take some form of qualifying exam which can channel them into an IMO training program.

And as far as the being amenable to brute force (relative difficulty for humans vs. computers): it seems that chess was comparatively easier for computers, IMO problems are comparatively easier for humans, and the game of Go is somewhere in between.

[okintheory]

These problems are literally already solved? Of course, the IMO problem designers make sure the problems have solutions before the use them. That's very different than math research, where it's not known in advance what the answer is, or even that there is good answer.

[snewman]

I'm saying they weren't solved until the problem composer (created and) solved them. They're not, in general, problems for which solutions have been lying around. So "these are problems that are already solved" isn't introducing anything interesting or useful into the discussion. The post I was replying to was trying to draw a contrast with chess moves, presumably on the grounds that (after the opening) each position in a chess game is novel, but IMO problems are equally novel.

It's true that IMO problems are vetted as being solvable, but that still doesn't really shed any information on how the difficulty of an IMO problem compares to the difficulty of chess play.