How to solve a 3×3 sliding puzzle step by step

Solve a 3×3 sliding puzzle by organising the first row, completing the left column beneath it, and rotating the final square. Plan the last pair of a row together so that a tile placed too early does not block its neighbour.

Use an unambiguous move notation

A dot means the gap. A named number means slide that tile into the current gap. This avoids mixing up a tile's direction with the opposite direction travelled by the gap. Every named tile must share an edge with the gap when its turn arrives.

The standard goal is ascending row order, ending with the gap at bottom right. Keep that goal visible while learning. A method based on regions is easier to understand when you know which cells you are trying to preserve and which remain available for routing the gap.

First, follow a complete short example

Start here:

1 2 3
4 . 6
7 5 8

Slide five up into the gap:

1 2 3
4 5 6
7 . 8

Then slide eight left into the gap. The result is the goal. This small example already demonstrates the essential idea: inspect the gap before every move, preserve the completed top row, and use the unfinished area to bring the last tiles home.

Now try a slightly longer starting position:

1 2 3
. 4 6
7 5 8

The tile sequence four, five, eight solves it. After four moves left, the position becomes the first example. Work through each intermediate board rather than treating the sequence as a magic formula. These are teaching examples, not a sequence for every possible scramble.

Build the first row

Bring one toward the top-left corner by putting the gap on the side where you want it to move. Route the gap around through unfinished cells, move one into it, and repeat until one reaches home. Then consider two and three as a pair rather than automatically fixing two in place.

The final pair needs a route into the row. If two is locked into its destination while three is trapped below it, you may need to move two again. That is a planning issue, not a failure of the whole puzzle. Work with the top-right area and the lower rows until the pair can enter in the proper order.

See a row-ending pair enter together

Here is a concrete pair setup, with one already protected:

1 . 2
4 5 3
7 8 6

Two is staged in the top-right cell, three is immediately below it, and the gap is beside two. Slide two left, then three up. The first row becomes correct and the gap exits into the lower area. In this particular example, sliding six up completes the board too.

The reusable idea is the pair's starting relationship: earlier target in the corner, later target below it, gap to the earlier target's left. To prepare it on another board, use the unfinished cells to route the gap and reposition the pair. Keep one protected and work backwards from those staging positions. The insertion moves are a precise local tool, not a sequence to apply before that setup exists.

Solve the left side of the remainder

Once the top row is correct, treat it as protected. Use the lower two rows to arrange four and seven in the left column. As with the row ending, plan these vertically adjacent targets together. Avoid leaving seven inaccessible beneath a prematurely fixed four.

For learning, pause before each short sequence and state its intended result. For example: the gap needs to get beside seven while the top row stays untouched. If no route exists under your current protection choices, revise the local pair plan instead of making unrelated moves across the whole board.

Finish the final square

With the top row and left column complete, the remaining cells form a small square. Legal moves around its perimeter cycle the remaining tiles and the gap. Rotate that cycle until the numbers and empty cell match the goal.

If the last square appears to need a simple swap of just two tiles, do not expect repeated rotations to perform that swap. Check whether the original board was solvable and whether earlier moves were all legal. A legal scramble from the goal cannot become unsolvable through legal play.

When the next sequence is unclear

Write down the local arrangement and list the legal gap moves. Reject an immediate reversal unless it serves a specific plan. Try a short route, note its result, and return to the starting arrangement if it does not help. This turns random shuffling into a deliberate search through a small set of states.

A hint can show a usable next move, but one suggested path is not automatically the shortest solution. Learn what the move is arranging: a gap route, a target tile, or a pair that needs to enter together.

Where to play

YIGE / 一格华容道 offers a 3×3 Easy route on HarmonyOS, alongside larger board sizes. Campaign hints and undo can help you study an unfamiliar position. Practise describing each move by tile number before trying to solve quickly.