Playing with cube mazes

We’re not talking about networks of passages inside a cube; that would give us those 3D mazes that we covered previously. Rather, here we’re considering mazes rendered purely on the surface of a cube.

Compared to cylindrical mazes, these are definitely a level-up. It’s true that they have some characteristics in common with cylinders (an ant on a cube could walk all the way around it), but there’s more to it. To help understand the difference, we need a simple way to visualize how a cube is constructed.

Let's start by picturing a cube, like a big cardboard box. If we were to unfold that box, taking it apart at the seams and laying it out flat, we’d end up with six square faces arranged something like the following figure. We’ll label the faces from 0 to 5 to make it easier to refer to them later.

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