Project Euler Forum

I'm working on Problem 812. I think I'm on the right track as I'm starting to see patterns and constraints in a brute force-ish search of possible $a_i$ for $f_N(x) = \sum_{i=0}^{N}{a_ix^i}$. I'm getting S(2)=6, S(3)=13, S(4)=30 and I am fairly confident that these are correct. But maybe I'm wrong.

However, I only find 57 solutions for S(5) instead of 58. Can anyone confirm that S(5) is indeed 58, or is this a typo in the problem description?

There isn't a typo. S(5) = 58, and all the other examples in the problem statement are correct.

philiplu wrote: Sun Aug 06, 2023 5:39 pm There isn't a typo. S(5) = 58, and all the other examples in the problem statement are correct.

Turns out my search space was only just too small for one of the coefficients. Exploring a different method of looking for solutions allowed me to find the missing one, without requiring many more calculations. Thanks again!