> But there's no reason to believe that the skills needed to solve math puzzles really quickly are either. I disagree. I think that having a strong sense of m

> But there's no reason to believe that the skills needed to solve math puzzles really quickly are either. I disagree. I think that having a strong sense of mathematical properties and numbers is more useful than any specific rote drilled into students. I see a lot of students up in precalc doing rote and not understanding at all why things work and that have no chance when you throw a curveball. On the other hand, the competitive math students are asking questions like: * What's the graph of this function look like? * What's it for the trivial case n=4 before I think about n=100? * Does symmetry or any other pattern collapse this down? * What properties do I expect the answer to have? Why does this direction "feel right"? The kids who excel in math competition and on the normal math academic track get there by playing with it and understanding it.