I watched a great video from 3Blue1Brown today, and it reminded me of what it was like to first wrap my head around the Monty Hall problem as a CS undergrad. The video, The Hardest Problem on the Hardest Test, is about a question from a Putnam Competition. Finding the solution is a matter of reframing the problem and changing perspective. Once viewed from the correct lens, the answer seems trivial.
From my post on 10/26/2021 when discussing the Monty Hall problem.
Instead of focusing on the probability that you pick the prize, focus on the probability that you initially pick a goat. If 2/3 of the time you pick a goat, and you are always shown one goat, switching results in you picking the car 2/3 of the time.
I know I've discussed this before on this blog, but this skill is something that I have been working to develop ever since exposed to it. In CS, we spend a ton of work on formulating efficient data structures and algorithms and then reframe the problem to fit these abstractions. This gets to the core of what I find so interesting about computer science, and seeing another example of it in the wild is always intriguing.