you do not need to remember state with the simplest solver:

- place your right hand on the right wall - walk forward, never letting your hand leave the wall - arrive at the exit

yes, you travel many dead ends along the way

but you are guaranteed to get to the end of a 'traditional' maze

Yeah I did the type where you start somewhere inside the maze and have to find the "treasure". Mainly because it was slightly easier to implement, but also had the nice side effect of not being solvable by that rule alone.

FWIW the LLMs were definitely not following that rule. They seemed to always keep going straight whenever that was an option. Which meant they would always get stuck at T intersections when both ways led to a dead end.