Working through many Olympiad math problems(pre-undergrad) I've found that simple applications of undergrad math will solve many of them. Does this trend go on? Can it be that Putnam problems are straightforward applications of math studied at grad level?
For those who still may not know to what I'm referring to, take the example of solving euclidean geometrical problems using Cartesian geometry. In this case you could say that the Descartes's theory replaced the "tricky" challenge of finding the right combinations of axioms to solve a euclidean geometrical problem.
Are there nice counterexamples to this?
Ultimately, could theory building replace "tricky problem solving"?