7x7 Sliding Puzzle Solver

When keeping track becomes the main challenge

A 7x7 sliding puzzle has 48 tiles and a blank. It is large enough that losing track of a single row can be more troublesome than deciding the next move. The center gives you plenty of temporary working space early on, but that space shrinks as completed borders accumulate. A good solution must organize the remaining region rather than repeatedly disturbing tiles that were already placed.

This page uses the same sliding puzzle solver with a 7x7 preset. The target is the numbered order 1 through 48 followed by the blank. Picture tiles obey the same movement rule: only a tile adjacent to the blank can enter it. Changing the artwork changes how you recognize pieces, not how the board can move.

Copy by rows, then verify the corners

Choose Edit start and open Type numbers. Enter 49 cells from the top-left corner across the first row, then continue with the second row. Use a space or comma between values. The blank is 0 or _, and each number from 1 to 48 must appear exactly once. Do not omit an empty-looking cell when transcribing a screenshot.

With seven entries per row, an accidental skip can look plausible for several rows before it becomes obvious. After typing, compare the four corners and the blank position with the source. You can exchange two cells in Edit mode to correct a misplaced label. To use a different finish, open More → Edit goal and enter that arrangement separately. Start and goal must represent the same set of pieces.

Lower bounds grow with tile travel

For any entered board, add the horizontal and vertical distances between each numbered tile and its target. This gives a lower bound on the required number of single-tile moves. If all 48 tiles in an example average four grid steps from their goals, the sum is 192; the board would need at least 192 single-tile moves. That calculation is a way to understand the scale, not a prediction for every 7x7 puzzle or a measured random-board average.

A long constructed answer can exceed that bound because tiles compete for the same corridors. The blank must travel to the useful side of a piece before moving it, and preserving a completed border can require an indirect route. Conversely, a large board with only a small local scramble can have a short answer. Compare the supplied move list with the actual starting pattern rather than assigning difficulty from the size label alone.

Recognize the active square

There are several common starting patterns. A board with the top row mostly assembled rewards finishing that boundary carefully, especially its final pair. A board with a completed outer row and column already has an active 6x6 square inside it. A puzzle with only the central region disturbed is best understood by matching those pieces to their goals and leaving the surrounding frame intact.

Another recognizable opening has one distant tile surrounded by pieces that appear correct. Following that tile directly can break several useful positions. Before moving, decide where the blank can circulate and which correct pieces may safely be displaced. Playback makes these temporary departures visible: a tile leaving its goal is not automatically an error if it creates a route for the next placement.

How a 48-tile route is assembled

The solver locks completed positions and searches only the remaining cells during each placement stage. It alternates between an outer row and an outer column, handling the last pair in each boundary together. These small searches track the target tile or pair plus the blank, instead of enumerating all arrangements of the 48 pieces. Repeating the process reduces a wide board to a compact final region.

The last 3x3 pocket is mapped to its own target labels and finished using a distance table. Its moves are then translated back to the original tile numbers. The joined route is simplified by removing adjacent moves that immediately reverse each other. The resulting answer is a fast construction for the whole board; it is not an exhaustive comparison of every route through the full puzzle.

Odd width and the order check

For the standard ordered goal on a 7x7 board, the numbered tiles must have an even inversion count. An inversion is a pair appearing in reversed target order when you read the board row by row and omit the blank. The blank's present row does not add a separate term for this odd width. For custom goals, the tool checks relative order against the goal you entered.

If a copied board fails the check, inspect similar-looking picture pieces or consecutive labels that may have been exchanged. Fix it deliberately changes a neighboring numbered pair and gives you a reachable arrangement; it does not make the original impossible arrangement solvable without changing it. Once the input is right, press Solve and use single steps or the playback speed control to follow the answer at a pace you can copy.