(Hi, delurking as my input may actually be useful here ;-) DS11 is doing reasonably well in competitions (for the latest, we await results; he probably won't quite make top 100 in the UK in a competition aimed at children 3 years older). He is lucky enough to be gainfully occupied in school maths lessons, though a fair bit of that is more about presentation than content, and probably spends an average of an hour a week working on maths problems at home, plus odd bits of time randomly thinking about stuff. Not much, in other words. This isn't much of a limiting factor now, but it will be soon; he'll have to decide whether it's worth it to him to spend more time. Here at least, and I think also in the US, you get to the actual selection process that leads towards IMO participation before you have to know more stuff, rather than just know it more deeply, than others your (assumed) age. So I wouldn't present it to him as that he must, but rather as that he could, and if he did, he might do better.
