Mazes4 levels
Printable mazes
A rectangular maze that is different each time you press New puzzle, in four sizes from easy to expert. It suits children, adults and anyone who wants a quick pencil puzzle with a printable solution.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
Each maze on this page is built fresh from a random seed, so no two prints are the same. The sheet opens on a Medium maze, one to a page, and you can change the size from there.
What prints
The title reads "Medium Maze", with a one-line direction to draw a route from the top through the paths to the finish without crossing a wall. The maze is a rectangle of square cells inside a heavy outer wall. A bold "Start" label sits over the opening at the top left, and a bold "Finish" label sits under the opening at the bottom right. The wall lines get thicker as the cells get larger, so easy mazes have bolder lines than expert ones.
The answer key is a separate page. It redraws the same maze with the solution path as a thick colored line, from the Start opening to the Finish opening.
The settings
- Difficulty: four sizes in cells across by cells down: Easy 8 × 10, Medium 14 × 18, Hard 22 × 28 and Expert 32 × 42.
- Mazes per page: 1 or 2. This page opens on 1.
With two to a page, each maze turns sideways to fill half the sheet, and the cell count changes to match: Easy becomes 10 × 6, Medium 18 × 11, Hard 28 × 18 and Expert 42 × 26.
How the maze is built
The generator uses a depth-first method often called a recursive backtracker. It starts in the top-left cell, moves to a random neighbor it has not visited, knocks out the wall between them, and keeps going until it reaches a dead end. Then it backs up to the last cell that still has an unvisited neighbor and continues from there. Every cell ends up connected, with no loops, so there is exactly one route from Start to Finish. This style tends to give long winding corridors and few short branches.
Tips for solving
Use a pencil. Try working backward from Finish for a few steps, since the dead ends near the exit are sometimes easier to see. Mark each dead end with a small cross so you do not return to it. For young children, a crayon on a larger maze is easier to control.
Worked example: a quiet-time packet
Ms. Chen builds a packet for a long drive. She sets Difficulty to Easy and Mazes per page to 2, prints six pages, and clips them with the key sheets removed. Her two kids, five and eight, take turns. The older child moves up to Medium, 14 × 18, and gets through it in about three minutes. She uses the key page only when an argument starts about whether a line crossed a wall.
Other maze pages
Easy mazes opens with two small mazes per page, and hard mazes opens on a 22 × 28 grid. For a longer puzzle, see mazes for adults.
Sources
- NRICH, University of Cambridge: Logic problems and puzzles nrich.maths.org