this is kinda nice

oh they have a bunch of similar ones too

@PhiNotPi I have a potential solution

Lets say there are M teams

and combinations are of size X

then the 1st combination would look like 1^1 mod M, 1^2 mod M, ... 1^X mod M

this obviously does no produce a combination (because there are duplicates), so we skip it and move on

the next one would be (2^1, 2^2, 2^3, ...2^X) (all mod M)

er...I think I have it backwards

the first combination is (2^1, 3^1, 4^1...), the second is (2^2, 3^2, 4^2...), and so on

I feel like this should produce an evenly spread set of combinations

but maybe not

hmmm...I think the bases have to be primes that don't divide M

instead of 2, 3, 4

@ASCII-only That was quite interesting.

AHHHHH *click*

@Feeds I thought this was pretty nicely done. I was actually thinking about how to find 2D zeroes in a way like the bisection method (1D) a few years ago but never really devoted much time to it.

It would've been nice for them to note that this method, like the bisection method, is not at all guaranteed to find every zero. Just at least one. Also, they didn't cover how to evaluate the boundary since you can necessarily only sample a finite number of points, so it's possible to accidentally skip over a zero on the boundary.

I did develop a method to find every zero of a 1D polynomial by evaluating its derivatives and using the bisection method starting with the 1-degree derivative and working upward. This "winding number" thing could perhaps be combined with that general technique to solve 2D polynomial equations...

When we think of polynomial approximation, we often assume that the context is an L2-norm. I just did some reading on polynomial approximation w.r.t. the L-infinity norm, which has quite an interesting result: en.wikipedia.org/wiki/Equioscillation_theorem

ELI25 plz