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Repair common Windows errors and clear accumulated junk for a smoother, more stable PC - no reinstall needed.Free scan · no reinstallTo solve a slide puzzle, move a tile next to the empty space into that space, one move at a time. First check that the board can reach its target; then make moves that bring tiles closer without repeatedly undoing your progress. The classic 8-puzzle is a 3-by-3 grid with tiles 1 through 8 and one blank, but the solvability check changes for wider boards.
What is a legal move in a slide puzzle?
A slide puzzle has numbered tiles and one empty square. A legal move slides one tile that shares an edge with the empty square into it. You cannot move a tile diagonally, jump over another tile, or move a tile that is not next to the blank.
In the classic 8-puzzle, the board is 3 by 3. Its usual target, called row-major order, is:
1 2 3
4 5 6
7 8 blank
The target arrangement is not universal: some games let you choose a goal state or use different tile labels. Check the displayed target before planning moves.
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- ✅【HOW TO PLAY？】Shuffle the order, randomly install it on the chessboard, move the squares to rearrange the numbers 1-24. Attention! You need to play on a horizontal tabletop, as the product is made of wood and does not have magnetism, it is easy to fall off and affect your experience!ers.
- ✅【Where is suitable for gaming？】This game is suitable for playing alone to relieve stress. It is recommended for children with autism, as well as for competing at family gatherings and parties. Simply slide the wooden block and see who completes the 1-24 sequence first. It is a very casual and educational toy
- ✅【What age group is suitable for？】For children aged 3 and above, it is recommended to start playing games from the beginner version. This product has three versions, beginner, intermediate, and advanced, which can correspond to different age groups. For adults, it is recommended to purchase the advanced version challenge directly from 1-24
- ✅【What material is used】All specifications of products are made of solid wood, with smooth edges that do not scratch hands. The products are non-magnetic and need to be played on a flat surface to prevent detachment. Attention, there may be a risk of ingestion of product components. Keep away from children aged 0-3 years old
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How to get unstuck
- Confirm the goal. Identify where each tile belongs and which square should be empty.
- Check whether the board is solvable. Some starting arrangements cannot reach the standard goal, even if every move is legal.
- Look for a tile that can move into the blank. Among the legal choices, prefer moves that bring tiles nearer to their target positions.
- Watch the tiles you have already placed. Avoid disturbing correct areas unnecessarily, but do not assume every temporary move away from the goal is a mistake; a tile may need to move to let another pass.
- Notice cycles. If the board returns to a position you have seen, retrace the moves or restart from the displayed state and choose a different legal move.
These are practical checks, not a guaranteed layer-by-layer recipe for every board. A specific sequence depends on the starting arrangement and target.
How to tell whether a board is solvable
For a square board, read the numbered tiles from left to right, top to bottom, skipping the blank. An inversion is a pair of tiles that appear in the opposite order from their numerical order—for example, 3 appearing before 2. Count all such pairs.
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Odd-width boards, such as the 3-by-3 8-puzzle
For an odd-width square board, the standard goal is reachable exactly when the inversion count is even. Thus, for the 8-puzzle, an odd count means the board cannot be solved to the usual row-major target.
Even-width boards, such as a 4-by-4 puzzle
For an even-width square board, inversion parity by itself is not enough. Add the blank’s row index, counting rows from zero at the top, to the inversion count. Under Princeton’s rule, the standard goal is reachable when that sum is odd. Do not use the odd-width inversion-only test on a 4-by-4 board.
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- ✅【HOW TO PLAY？】Shuffle the order, randomly install it on the chessboard, move the squares to rearrange the numbers 1-15. Attention! You need to play on a horizontal tabletop, as the product is made of wood and does not have magnetism, it is easy to fall off and affect your experience!ers.
- ✅【Where is suitable for gaming？】This game is suitable for playing alone to relieve stress. It is recommended for children with autism, as well as for competing at family gatherings and parties. Simply slide the wooden block and see who completes the 1-15 sequence first. It is a very casual and educational toy
- ✅【What age group is suitable for？】For children aged 3 and above, it is recommended to start playing games from the beginner version. This product has three versions, beginner, intermediate, and advanced, which can correspond to different age groups. For adults, it is recommended to purchase the advanced version challenge directly from 1-24
- ✅【What material is used】All specifications of products are made of solid wood, with smooth edges that do not scratch hands. The products are non-magnetic and need to be played on a flat surface to prevent detachment. Attention, there may be a risk of ingestion of product components. Keep away from children aged 0-3 years old
- ✅【Still worrying about what gift to give?】All specifications are packaged in customized color boxes with exclusive instructions, making them the best choice for gift giving
These tests apply to square sliding puzzles with the standard row-major target. If a game uses a different target or nonstandard rules, check its own solvability conditions rather than assuming the standard test applies.
A four-move 8-puzzle example
In the following board, 0 represents the blank:
Start:
0 1 3
4 2 5
7 8 6
One shortest route to the standard goal is to move tiles 1, 2, 5, and 6 into the blank, in that order:
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- Move 1 down into the blank:
1 0 3
4 2 5
7 8 6 - Move 2 up:
1 2 3
4 0 5
7 8 6 - Move 5 left:
1 2 3
4 5 0
7 8 6 - Move 6 up:
1 2 3
4 5 6
7 8 0
Each move uses a tile adjacent to the blank; no tile moves diagonally. Princeton University’s COS 226 assignment presents this start and four-move solution.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How a computer solver finds a solution
A solver treats every board arrangement as a state and generates neighboring states by sliding a legal tile into the blank. A* search ranks candidate states using the moves already made plus an estimate of the moves still needed. Princeton describes two estimates:
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- ✅【HOW TO PLAY？】Shuffle the order, randomly install it on the chessboard, move the squares to rearrange the numbers 1-15. Attention! You need to play on a horizontal tabletop, as the product is made of wood and does not have magnetism, it is easy to fall off and affect your experience!ers.
- ✅【Where is suitable for gaming？】This game is suitable for playing alone to relieve stress. It is recommended for children with autism, as well as for competing at family gatherings and parties. Simply slide the wooden block and see who completes the 1-15 sequence first. It is a very casual and educational toy
- ✅【What age group is suitable for？】For children aged 3 and above, it is recommended to start playing games from the beginner version. This product has three versions, beginner, intermediate, and advanced, which can correspond to different age groups. For adults, it is recommended to purchase the advanced version challenge directly from 1-24
- ✅【What material is used】All specifications of products are made of solid wood, with smooth edges that do not scratch hands. The products are non-magnetic and need to be played on a flat surface to prevent detachment. Attention, there may be a risk of ingestion of product components. Keep away from children aged 0-3 years old
- ✅【Still worrying about what gift to give?】All specifications are packaged in customized color boxes with exclusive instructions, making them the best choice for gift giving
- Hamming distance: the number of numbered tiles in the wrong position.
- Manhattan distance: the sum, for each numbered tile, of its horizontal and vertical grid distance from its goal position.
The blank is not counted as a numbered tile in either measure. With either stated priority function, the A* method is designed to return a solution using the fewest moves. A solver can also avoid immediately revisiting the board it just came from, which prevents a needless back-and-forth cycle.
This is useful if you want a computer to solve a board or are studying puzzle algorithms; it is not necessary to calculate a heuristic while playing by hand. For the move rules, parity tests, and solver specification, see Princeton University COS 226’s Slider Puzzle Assignment. For an additional introduction to inversion parity and search strategies, see 8puzzle.com’s 8-puzzle explainer.
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