Project Euler problem 227 - "The Chase" - is a nice example of a problem where the brute force approach is completely reasonable to reach for first, completely infeasible to actually finish, and directly points you at the right mathematical reformulation.

This is what we ended up with. Our full working notes are on the wiki at Project Euler/227.

The Problem

An even number of players sit around a table. Two players sitting directly opposite each other each start with a die. Each round, both players roll:

• Roll a 1 → pass the die to your left neighbor
• Roll a 6 → pass …