Project Euler 281 - Pizza Toppings

Official link:

Thought Process

This problem was really fun, but mathematically the most challenging problem so far.

I learnt the Cauchy-Frobenius Lemma in Abstract Algebra last semester, and I can without a doubt say it's the most confusing topic i've ever done, but I knew it would be perfect for this problem.

I brushed up on the Pólya enumeration theorem again, and managed to to find out that I was trying to solve was a subset of a problem involving what is referred to as a Necklace in Combinatorics. This page had an explicit formula which is stronger than what actually we need.

Before you read below I recommend reading these StackExchange questions, #1, #2, and the Multinomial Theorem which can ease you into what i'm doing next.

These values get enormous very quickly, to get the answer m ≤ 18, n ≤ 29 is all you need.

I used my phi function which is part of my essential functions.

Interactive Code

Enter a number (yourinput)

Code will output sum of all f(m, n) such that f(m, n) ≤ yourinput