6x6 Sliding Puzzle Solver

A larger board with an even-width rule

A 6x6 puzzle contains 35 sliding tiles and one blank. Its width creates a practical distinction from a 5x5 board: the row containing the blank matters when deciding whether an arrangement can reach the usual ordered target. A correct set of labels is necessary, but it is not enough. You can enter every number accurately and still have a board that cannot be solved by legal slides.

The sliding puzzle solver is set to 6x6 here. Its default goal places 1 through 35 in reading order and the blank last. Before entering a puzzle from another game, look at that game's completed board. A blank-first target or a different number order needs to be set through More → Edit goal.

Read six values at a time

Open Edit start → Type numbers and copy the board one row at a time. Each row has six cells, and the complete input has 36 values. Write 0 or _ wherever the blank appears; skipping it shifts every later cell and changes the puzzle. Spaces and commas are accepted. The labels 1 through 35 must each occur once, and the blank must occur once.

For a large board it helps to check the last value of each row before moving on: the sixth, twelfth, eighteenth, twenty-fourth, thirtieth, and thirty-sixth entries are the row ends. If the source is a picture puzzle, load the finished image with Photo and identify pieces by their goal locations. Similar patches of sky or fabric are easy to confuse. The editor also lets you exchange two cells directly, which is useful when correcting a transcription error.

A realistic way to discuss move counts

The number of legal arrangements grows far faster than the visible board area. Yet board size alone does not tell you how many slides your particular scramble needs. Add each tile's horizontal and vertical distance to its destination to obtain a lower bound. The blank contributes nothing to this sum. If 35 tiles average four grid steps away, the total is 140; at least 140 single-tile moves would be needed for that example. This is an arithmetic illustration, not a benchmark or a claimed average.

The actual route also has to provide space for tiles to pass. A piece that is already in its correct column may need to leave it temporarily, and moving the blank around a placed tile can add slides without reducing the distance total. The tool's reported length counts each individual tile entering the blank. Dragging a whole line by hand therefore corresponds to several single-tile moves, not one.

Openings that reward a plan

On a broadly scattered board, start by noticing where the top-row tiles are. It is often easier to bring them near their destinations before locking the row in place. If the first row is complete but the first column is not, treat the row as a boundary and reserve enough space below it to arrange the column's final pair. A board reduced to a 4x4 region is a useful midway checkpoint, although the full 6x6 route still includes all earlier placement work.

A common late-stage problem is a pair of tiles that seems simply reversed. Do not try to force that pair into place by swapping them in your mental model. Only neighboring tiles can slide into the blank. An apparent pair reversal may require a cycle involving other tiles, or it may signal an unreachable input. The parity check distinguishes those cases before you spend time replaying a route.

Placement searches instead of whole-board enumeration

The 6x6 solver constructs an answer by alternately settling an outer row and an outer column. Placement searches track the blank and the tile or tile pair currently being arranged. Other unsettled tiles can move through the available space, while completed positions are excluded from the search. Pair placement at the row and column ends avoids leaving an awkward last cell with no usable route into it.

After reducing the active region to 3x3, the solver finishes that region with a precomputed distance table and joins the moves into one replay. This approach aims for a fast, usable route. It does not compare all complete routes for the entire 35-tile board. Use Solve, then pause playback if you are copying the answer onto a physical puzzle. A direction arrow tells you which way the named tile moves.

The reachability test in plain terms

For the standard ordered goal, count inversions after leaving out the blank. Count the blank's row upward from the bottom, starting at one. On this even-width board, the sum of those two counts must be odd. Moving the blank vertically changes tile-order parity in the complementary way, so legal slides preserve the combined condition.

Custom goals are checked against their own arrangement. If the banner says the puzzle cannot reach the goal, recheck the copied rows and target first. Fix it changes two numbered tiles; it repairs the arrangement rather than discovering a route for the unchanged board. The difference matters when an external game does not allow you to exchange tiles.