Originally Posted by mithawk
Originally Posted by ChaosMitten
It depends on the level of competition, the child's potential, and how far the child wants to go. A very smart kid might make it to the Mathcounts national competition with very little effort or study outside of school, but they aren't going to win nationals. Same thing with doing well on the AMC tests vs making the Math Olympiad Summer Program.

Of course this depends upon the definition of a "very smart kid", but I don't think even a PG kid is guaranteed to get to MathCounts nationals unless you live in a non-competitive state. The tests have gotten dramatically harder over the years. For example DS can ace the AMC-10s or MathCounts nationals tests prior to 2010 and finds the AMC-10 tests before 2000 almost trivial. But his score on the recent AMC-10s is considerably lower.
Well, I didn't say guaranteed. I said might. And, of course, getting to nationals is a different story in a high population state with lots of high paying jobs and universities versus, say, Wyoming. Which I thought I covered with the first part of my first sentence about it depending on the level of competition.

I find your son's experience with the various years' test difficulties to be interesting. I don't have any real experience with the more recent years' tests. I would guess that a combination of the Flynn effect, the late 90s H-1B boom, and the founding of The Art of Problem Solving have all contributed to a significant increase in the competitiveness of math competitions in the US over that timeframe, necessitating a corresponding rise in test difficulty.