Heart-Shaped Maze

Heart-shaped mazes at five resolutions

The corridors are carved only into the cells that fall inside a heart outline, so every wall follows the silhouette and the finished page reads as a shape first and a puzzle second. The way in is at the top of one lobe; the finish sits down near the point.

That is the whole idea. It survives cheap paper and a tired printer, which is more than most Valentine's Day activities manage.

Resolution is the only real setting

Size is the grid the heart is drawn on: 20, 25, 30, 40 or 50 cells across. The heart takes the same proportion of the page at each one, so what changes is how fine the corridors are.

• 20 — chunky cells and a short route. A five-year-old manages it with a fat pencil.
• 25 or 30 — the middle ground, and the range where the outline still reads as a heart from across a room rather than dissolving into texture.
• 40 — a proper solve for an older child.
• 50 — very fine indeed. Lovely, and it wants a 0.5mm pencil and decent light.

Go too high for the audience and the shape stops reading. At 50 cells the walls are dense enough to swallow the outline.

Solution page and seed

The solution toggle adds a second heart with the route drawn through it. The seed reproduces an exact maze, which matters here more than on a plain grid: hearts vary a lot between generations, and if you find one whose route runs prettily through both lobes you will want it back.

What it is actually for

Valentine's Day classroom packs, obviously. It is also the shape people reach for on Mother's Day cards, on wedding tables, and inside an anniversary card that would otherwise have carried a printed verse somebody else wrote.

A blank heart maze printed at size 20 with a message written in the sea of white around it is a decent card. Print two, solve one against the other, and it is also a game.

How it is built

The heart mask is computed from the standard implicit heart curve at your chosen resolution, and a depth-first backtracker then carves corridors through the masked cells only. Every cell inside the shape is reachable and there is exactly one route between any two of them, so the maze is perfect in the technical sense as well as the sentimental one.

Print at 100% scale on A4 or US Letter. The shape's curved edges are drawn as small steps in the grid; letting the printer scale them softens the outline.

The same shaped-maze carver drives the animal-shaped mazes and the island maze, if you want a set of shapes rather than one.