This is a reasonable portion of what I did for math olympiads; the other parts were doing lots and lots of problems and acquiring a solid technical background.
One thing I worked on in particular is formulating good solution strategies, where I could see the general steps of a solution (or the steps of a good approach) without having to actually fill in all the details of the approach; this involves having good heuristics for figuring out what is true/false and what can be proved without too much effort (and then deferring the actual proof until later when all the pieces have come into place).
FTR I was a USAMO winner (top 12) in high school but didn’t make it to the IMO team. I did make the IOI team though. I’m currently coaching at the US IOI training camp for the next week, so I don’t have much spare time right now, but maybe when I have some I’ll share in a bit more detail the things I did (just a warning, this was before I started optimizing my behavior so while it apparently worked it was probably not an optimal trajectory).
This is a reasonable portion of what I did for math olympiads; the other parts were doing lots and lots of problems and acquiring a solid technical background.
One thing I worked on in particular is formulating good solution strategies, where I could see the general steps of a solution (or the steps of a good approach) without having to actually fill in all the details of the approach; this involves having good heuristics for figuring out what is true/false and what can be proved without too much effort (and then deferring the actual proof until later when all the pieces have come into place).
FTR I was a USAMO winner (top 12) in high school but didn’t make it to the IMO team. I did make the IOI team though. I’m currently coaching at the US IOI training camp for the next week, so I don’t have much spare time right now, but maybe when I have some I’ll share in a bit more detail the things I did (just a warning, this was before I started optimizing my behavior so while it apparently worked it was probably not an optimal trajectory).
(I expect top programming contests are harder/less feasible to train for at levels outside raw ability. It all happens too fast.)