Recursive Thinking (States)

I first learned of the "State" strategy from Andrew Cai, and it opened my eyes to a whole new world of possibilities. Come to think of it, states is but one way of recursive thinking. If we can break down a problem into multiple iterations of problems with a smaller scale but the same nature, recursive thinking can often do wonders to simplify the problems.


2019 AIME I Problem 5

2020 AIME II Problem 9 

2021 AIME II Problem 8  

2022 AIME II Problem 9

2023 AIME I Problem 11