Maze difficulty is usually labelled easy, medium and hard with no explanation of what those mean. We went looking for what actually varies, and found that the label was the least reliable part.
Two mazes, same size, wildly different
Generating mazes at a fixed size and measuring the length of the solution path, the spread was enormous. At the size we were calling 'easy', solutions ran anywhere from 65 to 167 cells — a 2.6× difference between the easiest and the hardest. At 'medium' the spread reached 3.7×.
Which means a child could be handed an 'easy' maze harder than the 'medium' one their sibling got. The label was a lottery ticket.
The fix is unglamorous: generate a batch and keep the one with the longest path. A maze costs about two milliseconds, so building twenty-five and discarding twenty-four is free.
| Level | Before | After | Spread |
|---|---|---|---|
| Easy | 113 cells | 171 cells | 2.6× → 1.3× |
| Medium | 184 cells | 341 cells | 3.7× → 1.3× |
| Hard | 365 cells | 545 cells | 2.3× → 1.3× |
The paths also wander through far more of the grid — from around a third of the cells to over half. A maze whose solution cuts straight across is a maze that mostly is not used.
Sizes by age
Ages 3–5 — 8×8 to 10×10
Wide corridors, a short path, a visible goal. At this age the skill being practised is following a line with a pencil without lifting it, not searching. If a child can see the end from the start, that is fine.
Ages 6–8 — 12×12 to 16×16
Dead ends become the point. A child this age can backtrack without frustration, and the moment of realising a corridor is a trap is the whole exercise.
Ages 9–12 — 18×18 to 22×22
Long enough that the solver starts planning ahead rather than following the first opening. This is where a maze stops being a motor-skill exercise and becomes a puzzle.
Teens and adults — 26×26 to 32×32
Several minutes of work. Fine for a book, too long for a classroom filler.
The trick every child finds
Put your hand on one wall and never take it off, and you will reach the exit of an ordinary maze. Always. We tested this against our own mazes at every size and the right-hand rule solved 100% of them.
Most children discover this by accident around age eight, and after that the maze is not a puzzle for them any more.
The obvious counter — adding loops so the maze is no longer one connected tree — turned out not to work. We built it, measured it, and the wall-follower still solved everything. Worse, the loops created shortcuts that made the solution shorter: a 'hard' maze went from 341 cells to 82. It made the puzzle easier while looking cleverer.
The thing that does defeat it is putting the goal in the centre rather than on an edge. Combined with loops, the wall-follower failed on 40–88% of attempts. It also shortens the path, so it is a trade rather than a free win.
If you are making mazes for a child who has worked the trick out, that is the direction to go — or simply hand them something else, which is often the better answer.
Printing
Give a maze the full width of the page. A maze printed small is not a harder maze, it is a maze solved with a pencil tip that does not fit the corridor, and the child gives up for a reason that has nothing to do with the puzzle.