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

Another approach that often works for these kinds of problems and does not require much intelligence:

Work out the first few cases by hand (1,2,6,20 in our case) and then look up the sequence on "The On-Line Encyclopedia of Integer Sequences" (OEIS):

https://oeis.org/search?q=1%2C2%2C6%2C20&language=english&go...

Ha. When I found that problem I draw the grids and paths from the example, left for a coffee and when came back I just look at the drawings at an angle and thought "well this is just Pascal's triangle". And the solution was obvious.

  me@localhost:~> bc
  d=1; for(i=21; i < 41; i++){d *= i;}; print d; print "\n";
  335367096786357081410764800000
  n = 1; for(i = 1; i < 21; i++){n *= i;}; print n; print "\n";
  2432902008176640000
  d/n;
  137846528820

I couldn't start Python for some reason, so I went 1337 and used BC, which comes preinstalled in every Unix-like OS. BC has a surprising advantage here since 40!/20! cannot be represented as a 64-bit integer since its value exceeds 2^64. That said, BC's stdlib does not provide the factorial function* - so I had to resort to using for-loops instead.

* - What it does contain is sine, cosine, exponential, log, arctan, and Bessel J (?!?!?!?!)

  let ans = 1
  for (let i=1; i<21; ++i) {
    ans *= (41 - i)
    ans /= i
  }

More like mathematical depression.

I am currently just going to college after high school and I was preparing for the JEE exam and I remember such a question was within the textbooks of maths itself.

At first glance of the question, I had imagined it to be hard but then I read through the solution and other comments to recognize that I had in fact done such a question previously and I had solved it independently during the class if I remember correctly or such classes of problems.

I also agree with the AI and spreadsheets part of thing for what its worth but I can only tell more when I get into job but I have heard such things from my senior brothers.

I feel like there has to be a right balance of complexity though, and for what its worth I think that there are so many other things that one optimizes later on in life with tangential benefits as well with real knowledge about real life use-cases and edge-cases and so much more! I feel like it would be hard to replace with AI as much as (some) people (mostly Marketing) want it to feel so.

I do hope that people don't atrophy their skills though and to solve some coding questions or make projects perhaps as well without LLM by hand if given/having the time. Not everything probably has to be done by the fastest or the most accelerated way as you wouldn't know the destination as it would be found along the way itself. I suppose just like life, so stay safe and have a nice day.

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this is like the most basic leetcode question. Some comments here sound like they need to brush up the basics