Guides & Articles
Everything we know about slide puzzles, organised by what you want to do — play a particular size, solve one, turn a photo into one, or read the maths behind why some boards are impossible.
What the 8 puzzle is, how to play, the standard top-row-then-left-column strategy, and why it is a foundational benchmark for AI search.
What the 15 puzzle is, where it came from, how to play and solve it, and how it compares to the 8 puzzle and the larger 24/35 boards.
What a picture slide puzzle is, why it suits children and casual play better than the number version, and what makes a picture work on a 4×4 or 5×5 board.
Step-by-step guide to making your own slide puzzle: pick a photo, crop it square, choose a size, and either play in an app or print and cut a physical version.
The 24 puzzle (5×5 slide puzzle) explained: rules, history, solve time, what changes from the 15 puzzle, and why optimal solvers need pattern databases here.
A history of 15-puzzle solving algorithms: BFS, A* with Manhattan distance, IDA*, walking distance, and additive pattern databases.
The 15 puzzle parity theorem: check if a board is solvable by counting inversions plus the blank's row. Clean proof and the Sam Loyd story.
How the 15 puzzle solver works: the human algorithm, A* with Manhattan distance, IDA*, walking distance, and pattern databases.
What the 35 puzzle (6×6 slide puzzle) is, who plays it, how long it takes, and why bigger boards become a research curiosity.
A worked solution of the 3×3 slide puzzle, showing the row-and-column method. The base case every larger sliding tile puzzle reduces to.
How to write an 8 puzzle solver: state representation, A* search, the Manhattan distance heuristic, and a sketch of the inner loop.
What slide puzzles actually train cognitively, what brain-training claims to treat with caution, and how they compare to sudoku and chess.
Custom sliding puzzles for gifts and personalization: which photos work, which board size to pick, and when to choose digital over physical.
Step-by-step guide to solving the 15 puzzle by hand: solve row 1, solve column 1, recurse into the 3×3 subpuzzle. Includes the corner-L manoeuvre.
The general method for solving any sliding tile puzzle by hand: row-and-column reduction with the L-shaped corner manoeuvre. Same at every size.
How image slide puzzles work: square cropping, on-demand tile rendering with clipping, and why downsizing to 1024×1024 is usually enough.
Where slide puzzles fit in the wider logic puzzle genre: comparison with sudoku, nonograms, kakuro, klotski, and chess puzzles.
How the Manhattan distance heuristic works, why it is admissible and consistent, and where it falls short for slide-puzzle solving.
What a number slide puzzle is, how it differs from picture variants, why numbers are the default for solvers, and when to pick them over photos.
How photo slide puzzles work: how images get squared and sliced, what photos slice well, and the privacy difference between cloud and on-device apps.
How to find a puzzle game without ads: what 'no ads' means in the fine print, IAP vs ad-funded apps, and the App Store signals to read first.
Why slide puzzles suit adults: short games, no skill ceiling, no notifications, no streaks. How to pick one without manipulative casual-game patterns.
Slide puzzles for children — cognitive benefits, board sizes by age (3×3 from 4–5, 4×4 from 7+), and what to look for in a kid-safe app.
What a slide puzzle solver does, when humans rarely need one, when developers always do, and how to choose between A*, IDA*, and pattern DBs.
Comparison of sliding puzzle solving algorithms: BFS, A*, IDA*, walking distance, additive pattern databases. Strengths and weaknesses of each.
The four techniques that solve any sliding tile puzzle by hand: row-and-column reduction, the L-shaped corner manoeuvre, empty-cell routing, endgame.
A guide to the sliding tile puzzle family: square grids, hexagonal variants, rotation puzzles, and the maths that ties them together.
How to check if a 15 puzzle is solvable, in plain language: count inversions, add the blank's row, check parity. What to do if you get a bad board.