They practically solve a very hard problem (it might take days for me to solve it) in 5 minutes. If that is not some supreme pattern matching then I don't know what it is.
Bunch of proof strategies used in math competitions are the same.
You have to have a giant knowledge of algorithms: fast fourier transform, bfs, dfs, iterative deepening, dijkstra, a*, sweep line algs, practically have to master dynamic programming (there's DP on trees, hidden markov model like DPs etc.), flood fill, topological sort, bipartite graph checks, kruskal, prim, edmonds karp, bunch of combinatorics, geometry algorithms.
data structures like segment trees, fenwick tree, suffix trees, etc.
you see where I'm going, there's a lot of memorization, and a lot of repetition (which improves memorization).
same thing goes for IMO, you have to do a lot of proofs, have to memorize and repeat a bunch of proof strategies in a huge number of mathematical areas.
