This is also me. I was a double CS and Math major in university and one of my favorite classes as a young lad was combinatorics and probability.. 25 years ago..
It's true, if you don't activate this area of your brain often, it's easier to brute force the solution and reach for the easy mechanical calculation. I can feel this when I'm refactoring code. Today, I just have Claude do it for me with a few instructions. Each day, I feel a tiny bit more ignorant about the actual framework's APIs, its abstractions, and its rules. But I still would rather do other things with my time.
As for the problem, luckily for me, this one was easy to derive if you remember factorials, permutations, and remember to account for duplicate patterns
Not to say it isn't useful to a CS education, but the only time I've ever ran into the well-ordering principle was to establish the foundation for mathematical induction proofs. Students usually learn this in discrete math for CS in undergrad. Then in many future undergrad courses that are algorithms focused, the proofs tend to use induction and no one really thinks of the WOP
It's so easy to bait me with this nostalgia. There is something mysterious and enjoyable about dialing-in or connecting to a server in the unknown. During those days, many things were not easily discoverable which added to the fun.
For a brief time, this extended to the early internet with IRC servers. I spent most of my early teenage years downloading warez, .wav music files, and trying not to be a n00b on #c while asking n00b questions
Now that I am an old man, I wonder what today's youth do that is equivalent to this fun nerdy culture? Maybe I can partake, LOL.
Hate to comment on the medium or writing style instead of the content but you're not alone. I understand the terms in the article in isolation or used in other fields, but it seems like the author is using a lot of technical metaphors. Or maybe I'm not their sophisticated audience.
It's true, if you don't activate this area of your brain often, it's easier to brute force the solution and reach for the easy mechanical calculation. I can feel this when I'm refactoring code. Today, I just have Claude do it for me with a few instructions. Each day, I feel a tiny bit more ignorant about the actual framework's APIs, its abstractions, and its rules. But I still would rather do other things with my time.
As for the problem, luckily for me, this one was easy to derive if you remember factorials, permutations, and remember to account for duplicate patterns