Sliding Puzzle

A sliding puzzle is a square grid of numbered tiles with exactly one empty space; you slide a tile next to the gap into it, one tile at a time, until the numbers read in order. It is one of the oldest and most recognisable logic puzzles in the world. A tile that sits directly next to the gap can slide into it; doing so leaves a new gap behind, which lets a different tile move next. There is no lifting and no swapping — every change you make is a single tile sliding into the one empty square.

What is the goal of a sliding puzzle?

Your goal is to arrange the tiles into numerical order, 1 to N, reading left to right and top to bottom, with the empty space finishing in the bottom-right corner. When the board reads 1, 2, 3… across each row in turn and the gap rests in that last cell, the puzzle is solved.

What sizes can you play here?

This page offers three sizes. The 3×3 board has eight tiles and is known as the 8 puzzle; it is the gentlest version and a great place to learn the moves. The 4×4 board has fifteen tiles and is the classic 15 puzzle — the size that started a global craze in the 1880s and still the one most people picture. The 5×5 board has twenty-four tiles, the 24 puzzle, and is a genuinely hard challenge that rewards a real method. Whichever size you choose, the rule is the same: slide tiles one at a time until the numbers run in order with the blank at the end.

The most reliable way to solve a sliding puzzle is the layer method: permanently lock the tiles around the edge of the grid to shrink the part you still have to solve, then repeat on what remains. Once a board grows past the 3×3 size, sliding tiles at random rarely gets you home — you need a plan. This approach is sometimes called solving by reduction.

How does the layer method work?

Start by completing the top row and the left column. Once those are correct, you treat them as finished walls and never disturb them again — every later move happens inside the smaller rectangle below and to the right. Solve the top row and left column of that smaller area next, and keep peeling off layers. Step by step the unsolved region shrinks from, say, 4×4 down to 3×3, then to a final 2×2 block in the bottom-right corner. That last square is special: its three tiles plus the gap can simply be rotated around until they click into place, with no clever sequence required.

How do you place the last two tiles of a row?

The one part that trips people up is the last two tiles of any row or column. If you try to drop them in one at a time, placing the final tile tends to kick the previous one back out. The fix is a small setup move: instead of putting the two end tiles straight into their target cells, park them just inside the corner — the second-to-last tile in the corner cell, and its partner directly below or beside it — then rotate the corner so both slide into their proper spots together. It feels like a magic trick the first time and becomes automatic with a little practice.

Throughout, remember that every move is reversible. If a slide makes things worse, you can always undo it by sliding the tile straight back. That safety net means you can experiment freely and never paint yourself into a corner.

Exactly half of all possible tile arrangements on a sliding-puzzle board are impossible to solve, but every board on this site is scrambled by legal slides from the solved state, so it is always solvable. Here is a fact that surprises most players: if you literally tipped the tiles out and dropped them back in random positions, there is about a 50% chance you would create a board that can never be put in order, no matter how brilliantly you play. The arrangements split into two camps — solvable and unsolvable — and there is no sequence of legal slides that crosses from one camp to the other. This split is a matter of parity, a deep property of how the tiles are permuted relative to the blank.

That is a nasty trap, and plenty of cheap physical puzzles and badly written apps fall straight into it: they shuffle the tiles randomly, hand you the board, and roughly every other puzzle is a dead end you can stare at for hours in vain.

This site never does that. Instead of shuffling randomly, every board is scrambled by making a long run of legal slides starting from the solved state. Because each scrambling move is itself a real, reversible slide, the finished position is always reachable — you simply retrace the path (or find a shorter one). The result is a firm guarantee: every puzzle you are given here can be solved. There are no broken boards, no impossible deals, and no wasted effort. If you are stuck, the answer is always out there waiting to be found.

To solve a 4×4 (15 puzzle), start with the top row — place tiles 1, 2, 3 and 4 in left-to-right order, using the empty space as your tool to steer each tile. Let us walk through the start of a solve so the layer method feels concrete.

How do you place the first tiles?

Begin with tile 1 and slide it into the top-left corner. Tiles are easiest to steer when you think of the empty space as your tool — you move the gap around behind a tile to nudge it where you want, one step at a time. With 1 parked in the corner, bring tile 2 into the second cell of the top row. So far so good, because neither tile interferes much with the other.

How do you finish the end of the row?

The end of the row is where the setup trick earns its keep. Rather than forcing tile 3 into the third cell and then tile 4 into the fourth — where placing 4 would shove 3 back out — you stage them. Put tile 3 into the top-right corner (cell four) and tile 4 directly beneath it, in the cell one row down. Now a single rotation of that corner rolls 3 leftwards into the third cell and 4 up into the fourth, completing the row as 1, 2, 3, 4 in one clean motion.

With the whole top row locked, you turn the board sideways in your mind and do exactly the same for the left column (tiles 1, 5, 9, 13), using the corner trick again for its bottom two tiles. Finish the top row and left column and you have reduced a 15 puzzle to a tidy 3×3 problem in the corner — and the same routine, one more time, leaves the final 2×2 to rotate home.

The 3×3, 4×4 and 5×5 boards are the 8 puzzle, 15 puzzle and 24 puzzle respectively — the same game at three sizes, with difficulty climbing steeply as the grid grows.

• 3×3 — the 8 puzzle (8 tiles). The friendliest version. With only eight tiles and one gap, you can often improvise your way to the answer, and it is the perfect board for learning how the empty space steers tiles and how the final rotation works. A worst-case scramble is solvable in at most 31 moves, and most need far fewer.
• 4×4 — the 15 puzzle (15 tiles). The classic, and the sweet spot for most players. It is big enough that random sliding stalls, so the layer method really pays off, yet small enough to finish in a few minutes once the technique clicks. This is the size behind the puzzle’s entire history and reputation.
• 5×5 — the 24 puzzle (24 tiles). A serious test. The extra layer means more rows and columns to lock down before you reach the centre, and a single careless move can cost you a lot of recovery slides. A clean, disciplined application of the layer method is essential here — improvising rarely ends well.

Whatever size you pick, tap New for a fresh scramble, or play the shared Daily puzzle to take on the very same board as everyone else that day.

The sliding puzzle was invented around 1874 by Noyes Palmer Chapman, a postmaster in Canastota, New York, and by 1880 the 15 puzzle had become an international craze. It has a richer back-story than almost any other pencil-and-tile game. Chapman arranged numbered blocks in a tray and challenged people to put them in order. The idea spread slowly at first, then exploded, sweeping through the United States and Europe as a genuine popular obsession — the kind of fad that filled parlours and newspaper columns alike.

What was Sam Loyd’s role?

The puzzle’s fame owes a great deal to the celebrated American puzzlist Sam Loyd, who promoted it relentlessly and, for years, falsely claimed to have invented it — a claim historians have since firmly debunked in Chapman’s favour. Loyd’s most notorious stunt was a standing offer of a $1,000 prize to anyone who could solve the so-called “14-15 puzzle”: the board fully in order except that the 14 and 15 are swapped, with the player asked to slide them back into the correct sequence.

Why was the 14-15 puzzle impossible?

The prize was perfectly safe, because that challenge is impossible. Swapping just two tiles flips the board’s parity, landing it squarely in the unsolvable half of all arrangements — no run of legal slides can ever fix it. Countless people burned hours (and reputations) chasing Loyd’s thousand dollars; not a single one could win, because the laws of permutation, not skill, stood in the way. It remains the most famous anecdote in the whole history of puzzles.

The hardest solvable 15 puzzle needs at most 80 single-tile moves with perfect play — its “God’s number” — while the 8 puzzle needs at most 31. If a puzzle is solvable, a natural question is: what is the most moves it could ever require, played perfectly? That worst case has a name borrowed from the Rubik’s Cube world — God’s number, the maximum number of moves needed to solve the hardest possible starting position with optimal play.

For the 15 puzzle, God’s number is 80 single-tile moves. This was settled by exhaustive computer search in 2011: no solvable 4×4 board, however fiendishly scrambled, needs more than 80 slides, and a handful of positions genuinely require all 80. For the smaller 8 puzzle, the figure is 31 moves. These are hard ceilings on the very worst cases — the vast majority of everyday scrambles fall well short, often solvable in a few dozen moves or fewer.

Knowing those numbers reframes the game. The puzzle counts your moves as you play, so you are not just racing to finish — you are trying to finish efficiently. A first solve might cost a couple of hundred slides as you find your feet; with the layer method and a little planning, that total tumbles, and chasing a lower count on the same board (or on the shared Daily) becomes its own quiet competition. Beating your personal best is often more satisfying than the first solve itself.

The same sliding-tiles game goes by many names — the 15 puzzle, fifteen puzzle, sliding tile puzzle, slide puzzle, number slide puzzle, mystic square, and (for the 3×3 version) the 8 puzzle. Different shops, books and apps pick different labels, but the mechanic never changes: slide numbered tiles into one empty space until they are in order.

Beyond the numbered original, two relatives are worth knowing:

• Klotski. A sliding-block puzzle built from blocks of different shapes and sizes rather than uniform numbered tiles. Instead of sorting numbers, your goal is to manoeuvre one particular large block through the others and out of an opening. The sliding-in-a-tight-space feeling is identical, but the irregular pieces give it a very different flavour of planning.
• Picture (image) sliding puzzles. Exactly the same grid and the same moves, except each tile carries a fragment of a picture instead of a number. Solving the board reassembles the scrambled image. These are a little harder than the numbered version, because you cannot rely on a clean 1-to-N order to tell you instantly where each tile belongs.

Learn the layer method on the numbered puzzle here and the skill transfers straight to picture versions, and partly to Klotski too.

Sliding puzzles are a tactile workout for spatial reasoning, planning and working memory, because every move forces you to plan a few steps ahead. Because each move is a single physical slide, the game keeps you constantly looking forward: to move this tile here, the gap has to be there first, which means moving those tiles out of the way. The layer method, once learned, turns that intuition into genuine strategy, and there is real satisfaction in watching a chaotic board fall into order under a method you control.

It is also a remarkably low-stress puzzle. There is no timer forcing you, no penalty for a wrong slide, and — crucially — every move is reversible, so you can never truly fail. That makes it easy to pick up for two minutes or settle into for twenty. The shared Daily puzzle adds a gentle daily ritual: the same board for everyone, a fresh one each morning, and your own move count to beat.

And if you enjoy ordering tiles by pure logic, the rest of this collection is a natural next stop. Number-driven deduction puzzles like Sudoku exercise the same patient, plan-ahead mindset, while picture-logic puzzles such as Nonogram reward the same eye for how the pieces of a grid fit together. The sliding puzzle is a perfect on-ramp to thinking in grids.

The key sliding-puzzle terms are tile, blank, solved state, layer (reduction), parity and God’s number; the costliest mistakes are sliding without a method and disturbing a finished edge. A few definitions make sliding-puzzle guides easier to follow:

• Tile. A single numbered square that can slide.
• Blank / gap. The one empty space; the only cell a neighbouring tile can move into.
• Solved state. Tiles in order 1 to N, blank in the bottom-right corner.
• Layer / reduction. Locking a completed row and column so the remaining puzzle shrinks.
• Parity. The hidden property that sorts every arrangement into solvable or unsolvable; swapping two tiles flips it.
• God’s number. The most moves the hardest solvable board can require with perfect play.

And the slips that cost the most time:

• Solving cell by cell with no method. Random sliding works on the 3×3 but stalls badly on bigger boards. Commit to the layer method early.
• Disturbing a finished edge. Once a top row or left column is correct, treat it as a wall — reaching back into it usually undoes your hardest work.
• Forcing the last two tiles straight in. The end of a row or column needs the corner setup-and-rotate trick; placing them one at a time just ejects the one you placed first.
• Forgetting the blank belongs bottom-right. A board can look ordered yet be unfinished if the gap is in the wrong place — always drive the empty space to the final corner.
• Fearing a wrong move. Every slide is reversible, so explore freely; you can always slide a tile back the way it came.