Hard Maze
Created for free at puzzleandprint.com
Hard mazes
Twenty to thirty squares, with the solution on its own page.
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Hard Maze, Solution
Created for free at puzzleandprint.com
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Four mazes, each a different size. Every one is a two-page PDF, the maze, then the solution on its own page.
Hard maze, twenty20 × 20 squares · MediumDownload PDF ↓
Hard maze, twenty-four24 × 24 squares · HardDownload PDF ↓
Hard maze, twenty-eight28 × 28 squares · HardDownload PDF ↓
Hard maze, thirty30 × 30 squares · HardDownload PDF ↓Every sheet here is free to print as often as you like. If one saved you time, the tip jar is on Ko-fi.
Past about twenty squares a maze stops being something you solve by looking and becomes something you solve by working. The route doubles back on itself, the dead ends get long enough to be convincing, and you generally need a pencil rather than a finger.
The four sheets here run from twenty to thirty squares. Thirty is the largest size that still prints with corridors wide enough to draw a line in on Letter paper, which is why the generator stops there rather than going higher. A bigger maze on the same sheet is not a harder puzzle, just a fiddlier one.
Difficulty in a maze comes from how often you can go wrong and how far a wrong turn takes you, and only the first of those reliably grows with size: from the smallest sheet to the largest there are 35, 65, 76 and 87 dead ends. Every maze here is still a perfect maze (fully connected, exactly one path between any two points), so there are no tricks, no loops that waste your time, and no unreachable corners.
These suit adults, older children, and anyone who wants something absorbing that is not on a screen. The solution prints separately, so you can put it face down and stay honest.
Where the longest dead ends hide in the hard mazes
On the Twenty-four and Thirty hard mazes the longest dead end opens within six squares of the way out, so the biggest trap on each sheet sits right beside the finish. On the Thirty, five squares short of the exit, one turn leads into a branch of 311 squares, about a third of the maze, and the longest path through it runs 183 squares before it stops. On the Twenty-four the same thing happens six squares from the end: a branch of 226 squares, with a path of 152 squares into it, not far short of the 181-square route itself.
The other two sheets place their traps earlier. On the Twenty-eight the largest branch, 304 squares, opens about three quarters of the way along a 335-square route, and on the Twenty the biggest is a branch of 76 squares opening about three fifths of the way along. That is why the time a sheet takes depends so heavily on one decision: on the three larger sheets, a solver who chooses correctly at the fork that matters finishes briskly, and one who does not has more than a hundred squares to walk before finding out. Looking down both corridors from a fork before committing the pencil saves more time here than drawing quickly does.
Does the hard setting make a maze harder or only bigger
The hard setting makes a maze bigger, not different: the maze maker carves every maze the same way whatever the difficulty, and choosing Hard simply sets the grid to 26 squares. The carving starts at the way in and moves to a random neighboring square it has not visited, again and again, until it is boxed in; then it backs up to the last square with an unvisited neighbor and sets off from there. That method makes long, winding corridors and comparatively few forks. The Thirty sheet's 900 squares contain 86 places where three or more corridors meet, and the true route passes 26 of them.
On the ready-made sheets the labels follow the grid: the Twenty is marked Medium and the other three Hard, and the label changes nothing about how the maze was carved. Size does not even guarantee length, because the generator does not aim for a route of any particular length, and the Twenty's route of 211 squares is longer than the 181 of the Twenty-four. What size does guarantee is narrower corridors, about 9 mm across on the Twenty and 6 mm on the Thirty, and more squares in which to go wrong. For an adult that is the real difference between the four: how much maze there is to get lost in, not a cleverer kind of maze.
Common questions
Why does the generator stop at thirty squares?
Because thirty is the last size at which a pencil line still fits comfortably between the walls on US Letter. The maze is fitted to the width inside the page margins, so on the Thirty each square is about 6 mm and leaves a little over 5.5 mm of white between the printed walls. A thirty-first square across would take about a fifth of a millimeter off that, so the size control on the maker stops at thirty.
Can these be solved without a pencil?
Rarely past about twenty squares, because there are too many branches to keep track of by eye. The true route on the Twenty has 16 side branches leading off it, the Twenty-four 15, the Twenty-eight 27 and the Thirty 26, and every one of them ends in a dead end somewhere. A light pencil check mark at the mouth of each branch already tried stops you walking the same one twice.
Does keeping one hand on the wall solve these hard mazes?
Yes, every time. Each maze here has exactly one route, no loops, and both openings in the outer wall, so a pencil that follows one wall without ever leaving it must come out at the way out. It is rarely the quick way, because it walks into every dead end on that side first, and on the Thirty sheet that can include a branch of more than 300 squares.
Want to know when new printables go up?
New printables when they go up, mostly seasonal, a few times a year.