Tile Shift: plan the empty square, then move the tile
A two-move example shows why the blank is your route through the board, and how a small plan prevents unhelpful back-and-forth slides.
Read a move in both directions
When you slide a tile into the empty square, two things happen: the number changes position, and the empty square takes the number’s old position. Paying attention only to the number hides half the move. Your next available choices depend on where the empty square finishes, so a useful plan names both destinations.
Tile Shift’s arrow keys describe the empty square’s movement. Pressing Down brings the tile below it upward. This convention can feel reversed if you are watching the numbered tile. Before planning a sequence, locate the blank and describe the route from its point of view.
Work through a position with only two moves left
Imagine this board, with slashes separating its rows: 1 2 3 / 4 blank 6 / 7 5 8. The top row is complete. Tile 5 belongs in the centre, while tile 8 needs to move left along the bottom row. The empty square is exactly where 5 needs to finish.
Move the blank Down. Tile 5 slides up into the centre, leaving the blank between 7 and 8. Then move the blank Right. Tile 8 slides left, and the empty square reaches the bottom-right corner. The two moves solve the position without disturbing any tile that was already correct.
Ask where the blank must arrive next
For a more complicated position, choose one tile and one immediate destination. Ask which neighbouring square must be empty for that slide to happen. Then look for a route that brings the blank there. This separates preparation from the slide you actually want, instead of treating every legal move as equally promising.
The shortest route for the blank can still disturb useful work. Compare the route with the positions you want to protect. A slightly longer route around an unfinished region may be easier to reason about than cutting through a completed row and having to rebuild it.
Notice when movement produces no new choice
Sliding a tile into the blank and immediately sliding it back restores the same board. Two moves have passed, but the available choices are unchanged. Such a reversal can be useful when correcting a mistake; it becomes unhelpful when you repeat it without changing your plan.
Before reversing, state the reason for your previous slide. If you cannot name a destination it helped prepare, use that as a signal to pause. Choose a small target such as bringing the blank below tile 5, rather than the vague target of making the whole board look tidier.
Treat this as a planning habit, not a complete solver
Local plans do not guarantee that the remaining tiles will cooperate. Sometimes a tile must leave its correct position so another tile can pass. Undo is useful for comparing two short routes from the same position, while Restart lets you reconsider the original puzzle with what you have learned.
Judge a plan by the position it creates and the next move it makes possible. A rising move count is not proof of failure, and a low count does not explain a strategy by itself. The practical goal is to replace repeated guesses with a sequence you can describe and check.
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