Why didn't Harry use the right-hand-rule (or other methods) to solve the Triwizard maze?

As with most labyrinths with conjoined borders, there are age-old methods of solution, such as simply placing one hand on a wall and proceeding through the maze without removing it until you come to either the centre or the exit (right-hand-rule). Yet IIRC Harry neglects to try this, let alone address any traditional maze-solving methods at all during the Third Task.

I'm sure the case is different for enchanted mazes, but I was wondering specifically whether this was actually addressed canonically at all, either by J.K. Rowling or the directors/screenwriters (books or movies).

Answer

Not addressed anywhere in canon, as far as I'm aware. With that in mind, let's proceed with speculation.

Even if we ignore the fact that the structure of the maze may potentially be changing (because it's magic), there are several factors that would cause Harry not to use a maze solving algorithm:

He's probably not aware of them. I can't imagine Harry did a lot of maze solving prior to coming to Hogwarts because the Dursleys aren't the kind of people who take him places. He's also not portrayed as the kind of person who would study maze solving algorithms for fun.

The wizarding world - including Harry by his fourth year - have a tendency to prefer magical solutions over more mundane ones, to the point where they will completely overlook potentially better solutions that don't involve magic.

The Triwizard Task was a race. A maze solving algorithm may eventually lead Harry to his goal, but eventually doesn't necessarily cut it when you have to be first.

The Task wasn't designed to primarily test their ability to solve mazes. The primary purpose was on testing the Champions' ability to react to different situations and solve different types of problems. The maze aspect was ultimately secondary.

Harry knew he needed to get to the centre of the maze, and therefore prepared a spell that would keep him on the right track (supposedly - I have doubts about whether what's described in the books actually makes any sense). Being constantly pointed in the direction you need to go is possibly more efficient than a maze solving algorithm.

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