Five maze shapes, and what each one does to the solving

A maze's shape isn't decoration. Change the grid under it and you change how many choices a junction offers, how your eye scans the page, and whether the solver is deciding or tracing.

Here's what each of the five does, and who each one is for.

Square: four ways out, and your eye can scan

The familiar one. A grid of squares, walls between them, an arrow in and an arrow out.

What makes it readable is that your eye can run down a column or along a row. You can take in a whole region at a glance and rule it out, which is why a square maze of a given size feels faster than any other shape with the same cell count. At a junction you arrived by one side, so at most three ways on are left.

It's also the only shape where the corridor width is simple to reason about. At 40 by 40 on a letter page a corridor is about five millimetres, which is fine with a pencil and miserable with a crayon. If you're printing for a four-year-old, drop a size rather than thickening the walls.

Hexagonal: six sides, nothing straight to follow

A honeycomb. Six neighbours per cell instead of four, so a junction can offer five ways on, and the corridors slant as well as turn.

Two things make it harder than a square maze at the same cell count, and only one of them is the arithmetic. The second is that there's nothing straight to scan. A square grid lets you check a column in one look; a honeycomb makes you trace every corridor to find out where it goes. Solvers who've run out of square mazes usually find a hexagon the next real step up, and they find it without the page getting any bigger.

Triangular: three sides, so junctions are rare

Triangles pointing up and down in alternating rows. Three sides per cell, which means most cells have one way in and one way out.

That changes the rhythm rather than the difficulty. You spend long stretches simply following a corridor, then arrive at a junction that matters. It's less about choosing and more about tracing, which suits a solver who finds a dense square maze fussy. The grid is also taller than it is wide for a given cell count, so these sit well on a portrait page with room left for a title.

Circular: solved inward, and the rings have to subdivide

Concentric rings cut into wedges. You enter at a gap in the rim and work in to the hub, so progress is counted in rings rather than in distance across the page.

The interesting engineering problem here is that the outer ring is several times longer than the inner one. Give every ring the same number of cells and the middle becomes slivers while the rim becomes caverns, and the result reads as a target rather than a puzzle. So a ring splits whenever its cells would get too wide, which keeps every corridor roughly as wide as it is tall from hub to rim.

That radial journey also has a consequence worth knowing if you're grading mazes: the route of a circular maze is structurally shorter relative to its cell count than a square maze's is, which is one of the corrections we had to make when we measured what makes a maze hard.

Picture shapes: the outline does some of the solving

A square-grid maze carved to fill a silhouette. A heart, a star, a crescent moon, a cat, a tree.

Mechanically it solves like a square maze, but the outline removes branches for you. A corridor that runs out into the tip of a star has nowhere to go, and once a solver notices that, whole regions of the page stop being candidates. The star is the most forgiving of the silhouettes for exactly this reason.

The crescent is the opposite. It's thin everywhere, so the maze has no width to spread into and the route has to run most of the way around the arc. For its cell count it produces the longest solution of any of our shapes.

There's a sampling problem underneath all of them. Carve a shape at a small enough grid and the tip of a star or the horn of a crescent can sample into an island the solver could never reach, which would break the one promise a maze makes. So every silhouette is reduced to its largest connected region before anything is carved. It's the kind of guarantee you only notice when it's missing.

Picking one

For a child under seven, square. The familiarity is doing work, and novelty is not what makes a maze fun at that age.

For an adult who has had enough square mazes, hexagonal at the same size they already like. It's the cheapest real increase in difficulty available, because it doesn't make the page any denser.

For a card, a classroom wall or anything that has to look like a gift, a picture shape at small or medium. A heart at the giant setting is a lovely object and a forty-minute job, which is the wrong trade for something tucked inside a card.

All five are in the printable maze generator→, free, with the solved route on the second page. If you want a whole book in one shape, that's what the KDP maze maker is for, and how to make and sell maze books on KDP covers the publishing side.