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Slide 15 Method: Solving the 15-Puzzle Layer by Layer

Updated October 2026

Slide 15 is the four-by-four sliding puzzle: fifteen numbered tiles, one gap, and a target order that runs 1 to 15 across the rows with the gap in the bottom-right corner. Anyone can solve it eventually by pushing tiles around. Solving it quickly takes a fixed method, a few memorised manoeuvres and a habit of planning before you touch the board. This guide explains how the game builds its scrambles, how your time is measured, and a layer-by-layer method that works on every position.

What you are up against

Each new game starts from the solved board and makes 80 random slides, never undoing the move it has just made. It then adds up how far every tile sits from its home square and keeps the board only if that total is in a narrow middle band (26 to 32 squares); otherwise it scrambles again, so no board is unusually easy or unusually hard. Because the scramble is built only from legal slides, every board can be solved. Roughly half of all possible arrangements of the tiles cannot be solved at all, but you will never meet one of them here. If you reach the very end and seem to need two tiles swapped, a tile somewhere else is out of place.

Eighty random slides mix the board well. In our simulation of 1,000 scrambles, the shortest possible solution ranged from 30 to 54 moves, with a median of 42, and nine boards in ten needed between 36 and 48. A typical starting board in our simulation had only one or two tiles already in their home squares. No human method finds the shortest solution, so expect to use more moves than that, often around twice as many. The goal is to keep that number low without slowing down to think.

The clock and the controls

The timer starts on your first slide, not when the board appears. That means you can take as long as you like to look at the board before moving, which is the best moment to find tiles 1 to 4 and plan how to bring them up. From the first slide onward the time is measured to the millisecond and shown in tenths of a second. Your score is that time, and lower is better. The move counter is shown for your interest, but it does not change your score; extra moves only cost you the time it takes to make them.

Only a tile directly beside the gap moves, and each tap moves exactly one tile. Tapping a tile two places away does nothing, so a long run of slides is a series of single taps along the line. Tiles that can move are drawn slightly lighter, and any tile sitting in its correct square turns green, which is a handy check that a finished row really is finished. The clock stops the moment the last tile lands.

The layer method

Solve the board in this order and never disturb a finished part:

  1. Top row: 1, 2, 3, 4.
  2. Second row: 5, 6, 7, 8.
  3. Left column of the bottom half: 9 and 13 together.
  4. Next column: 10 and 14 together.
  5. The last two-by-two block: 11, 12 and 15, which only needs the three tiles cycled round.

Working by rows first and then by columns means the space you are working in keeps getting smaller while always staying at least two squares wide, which is the minimum room the manoeuvres need. Doing the two bottom rows as columns, not rows, avoids the awkward case of finishing a row with nowhere to park tiles.

Placing the first tiles of a row

Moving a single tile is a matter of bringing the gap to it and then walking the tile one step at a time. To move a tile one square in any direction, first put the gap on the far side of it in that direction, then slide the tile into the gap. To move it again, the gap has to travel around the tile, which takes extra slides. That is why moving a tile sideways along a row while keeping it there is expensive. It is usually quicker to bring the tile to its column along the row below and then lift it into place.

Tiles 1 and 2 (and 5 and 6) go straight into their squares. Keep the gap below or beside the area you are working on so that you never have to drag it through a finished row.

Finishing a row: the corner pair

The last two tiles of a row cannot be placed one after the other, because placing the third tile leaves no room to bring in the fourth. Place them as a pair instead. For the top row, put tile 4 in the square where 3 belongs and tile 3 directly below it. Then bring the gap round to the top-right corner without disturbing them. Two slides finish the job: slide 4 right into the corner, then slide 3 up into the space it leaves. The same set-up finishes the second row with 8 and 7.

The bottom two rows use the same idea turned on its side. Put 13 in the square where 9 belongs and 9 to its right. Bring the gap to the bottom-left corner, slide 13 down, then slide 9 left. Then do the same with 14 and 10 in the next column. If the second tile is already sitting in the corner it should go into, the pair cannot be formed directly. Move it out at least two squares away, set up the pair properly, and accept the cost. Trying to force it from a bad start nearly always takes longer.

The final cycle

With two columns of the bottom half done, only 11, 12 and 15 remain in a two-by-two square together with the gap. In this block the tiles can only travel round the square in a loop, clockwise or anticlockwise. Look at the order of the three numbers going round the loop, decide which direction brings them home in fewer steps, and spin the gap that way. It never takes more than a handful of slides. Because the scramble is always solvable, the three tiles will always line up correctly.

Getting faster

Your best time is stored on your device, and finished times can be saved to the Hall of Fame. A clean layer solve with confident pair set-ups beats a lucky shortcut almost every time.

▶ Play Slide 15 Slide the tiles into order, then beat your time.