MazesHard
Hard mazes
One large 22 × 28 maze per page, with 616 cells and a single route from Start to Finish. It is meant for older children and adults who want a challenge that takes a few minutes.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
The Hard size packs 22 cells across and 28 down, which is 616 cells, onto one page. Paths are narrow, and there are many places to take a wrong turn.
What prints
The sheet is titled "Hard Maze" and the direction asks for a drawn line from the top, along the paths, to the finish. A "Start" label stands over the opening at the top left, and "Finish" sits below the bottom right. Wall lines are thinner than on Easy because the cells are smaller, and the maze is centered below the heading. The answer key shows the same maze again with the solution marked as a heavy colored line.
The settings
- Difficulty: set to Hard (22 × 28 cells). Expert is larger still, at 32 × 42, and Medium is 14 × 18.
- Mazes per page: one to start, with two as the alternative.
At two per page, a Hard maze turns on its side and becomes 28 × 18, which is 504 cells, so each one is a bit smaller than the full-page version.
How it is made
A recursive backtracker builds the maze. It starts at the top-left cell and keeps moving to a random unvisited neighbor, removing the wall between them, until it hits a cell with nowhere new to go. It then backs up and tries another side. When every cell has been visited there are no loops, so exactly one route links Start to Finish. Mazes made this way tend to have long, twisting corridors, and the dead ends can run a long way before they stop.
Strategies
Do not follow every branch in order. Look at the Finish end first and scan back, because dead ends near the goal can often be ruled out quickly. Mark a dead end as soon as you find it. A thin pen or sharp pencil helps in narrow corridors. If you print on plain paper and want to reuse the maze, slide it into a sheet protector and use a fine dry-erase marker.
Timing yourself is optional, but it makes a good game: each person solves the same printout, and the one who gets from Start to Finish first, without crossing a wall, wins the round.
Worked example: a family road-trip contest
The Navarro family prints four Hard mazes, one per page, and keeps the answer pages in an envelope. At a rest stop, two cousins race on the same maze, each with a different color pen. One of them finds, after ten minutes, that the opening corridor leads to a dead end, so she goes back to the first fork. The other gets through in about eight minutes. They check the line against the key page and mark where they turned wrong.
More like this
For a bigger challenge, try mazes for adults, which opens on Expert. The printable mazes page opens on Medium. If you like finding paths in grids, hard sudoku is a number puzzle at the same level.
Sources
- NRICH, University of Cambridge: Logic problems and puzzles nrich.maths.org