Related — these videos give a sense of how someone might actually go about thinking through and solving these kinds of problems:

- A 3Blue1Brown video on a particularly nice and unexpectedly difficult IMO problem (2011 IMO, Q2): https://www.youtube.com/watch?v=M64HUIJFTZM

-- And another similar one (though technically Putnam, not IMO): https://www.youtube.com/watch?v=OkmNXy7er84

- Timothy Gowers (Fields Medalist and IMO perfect scorer) solving this year’s IMO problems in “real time”:

-- Q1: https://www.youtube.com/watch?v=1G1nySyVs2w

-- Q4: https://www.youtube.com/watch?v=O-vp4zGzwIs