It’s my game plan for keeping my brain active in retirement. Been heavily involved for the past 7 years. Been at the 100% solved level since summer 2023, though I’m back to one away the past couple weeks - PE910 is _hard_
I've got a bachelor's in math, but that's 40+ years ago. I had intended to go on for a PhD in math, but fell into computers instead - programming was easier and way more lucrative, even in the early 80s. Once I was retired and found my way to Project Euler, it became an obsession, tickling that desire to go deeper into math that I had in my college days.
I attacked roughly the first 250 problems in order. The early problems build on each other to introduce new topics. I also got good at figuring out the right search term to find some random paper in number theory, combinatorics, probability, whatever.
Later problems introduced new, more niche areas, like chromatic polynomials and impartial & partisan game theory. But by then, I found it much easier to figure out what part of math a problem was based on and how to find relevant literature.
It helps to be really really stubborn, and to have the patience to let a problem stew in my brain, sometimes for weeks at a time. That seems to help lead to that Eureka moment.
One other thing - can't believe I forgot to mention this: once you solve a problem, read the solvers' thread in the forum! I learned so much by doing that, which fed into success on later problems. The link will be at the bottom of the problem page once you've solved it.
There are some much later problems where some obscure technique gets mentioned, even though the problem is doable without that technique. But then later on, there are other problems where that technique is practically required. I can think of multiple 100% difficulty problems which were actually much easier than that for me, because I had already seen and tried out the techniques that enable a fast solution.
And sorry, not going to mention any of those techniques. A lot of the fun I have in solving PE problems is that incremental increase in knowledge as time goes on.
As a class of problems, I'd say the combinatorial game theory ones are my favorites. There are a lot of impartial game theory problems - look for problems mentioning Nim or stone games. They build on each other nicely, from the mid 300s on. The site has been getting into partisan game theory problems in the past year, which finally got me to buy "Winning Ways For Your Mathematical Plays", vol 1, and "Lessons In Play". I find pretty much any problem with John Conway's influence fun to do.
As for a single problem, I'm fond of PE589, "Poohsticks Marathon". That was my 501st solution, two years after first attempting it (solved 5 years ago, yikes). I like it because it's a problem with a 95% difficulty rating, so very tough, but the development team slotted it in as an easy problem (problems normally get scheduled in batches of 6 with a cadence of medium/easy/medium/easy/medium/hard). Once I solved it, I agreed that it was relatively easy, in that it uses techniques introduced by early PE problems, but something about it makes using those techniques unexpectedly difficult.
I have been working on PE problems for most of 10 years. One thing I would sort of like to do is make a library (mostly I have been using python) for some of the more common functions. Do you have anything like that?
I do, but there's nothing too obscure in it. Efficient prime number sieve, prime factorization using trial division, generating list of divisors from the prime factorization, modular inverse via Euclidean algorithm, Chinese Remainder Theorem.
I also have some stand-alone modules, one to solve generalized Pell equations, another to find a polynomial given a sequence via the differences (e.g. 2, 5, 10, 17, first differences 3, 5, 7, second 2, 2 is enough to find n^2+1). There's another to find the closed form for a sequence as a linear recurrence.
Some solvers have much more extensive libraries, but I tend to grab bits of code from old solutions to reuse on the fly.
