How the slide puzzle works
The picture is divided into an even grid — 3 × 3 up to 6 × 6 — and one corner tile is taken away to make a gap. Only tiles next to the gap can move. Tap one, or swipe it towards the gap, and it slides across. If you tap a tile two or three places away along the same row or column, the whole line moves in one go, which saves a lot of tapping on bigger boards. Arrow keys work too.
When every tile is back in place, the missing tile fades in and the picture is complete. The counter shows how many moves you used, and your best time and move count for each size are kept.
Why every deal is solvable
Mix the tiles of a slide puzzle at random and there is a fifty-fifty chance the result can never be finished, however long you try. A mathematical rule, based on counting how many tiles are out of order and where the gap is, tells the two halves apart. The game uses that rule, so every shuffle you get here has a solution.
A reliable order of work
Start with the top row, then the left column. Each finished row or column turns the puzzle into a smaller one, so a 4 × 4 becomes a 3 × 3 and you finish on familiar ground. The last two tiles of a row are the tricky part: park the next-to-last tile at the end of the row first, bring the last one underneath it, and then rotate the pair into place together.
On the last two rows, switch direction and work column by column, two tiles at a time. If the picture has large areas of similar colour, turn on the numbers; they show where each tile belongs without changing the puzzle.
Sizes and pictures
3 × 3 has eight tiles and is a quick warm-up. 4 × 4, the classic size, has fifteen and asks for a plan. 5 × 5 and 6 × 6 are long puzzles for patient players; the hint button will suggest a move, and on the largest boards, when the search runs out of room, it highlights a misplaced tile instead. Pictures with one big clear subject, like the harbour boats or the lighthouse, are the friendliest choice for a first try.
Questions
Is there always a solution?
Yes. Every shuffle is checked with the solvability rule before the board appears.
What do the numbers do?
They show each tile's home position. They do not change the puzzle; they just help when tiles look alike.
Can I shift a whole line in one go?
Yes. Pick a tile in line with the empty square but further away, and every tile between them shifts in one go. Each tile that moves counts as one move.
Does the hint solve the puzzle for me?
No, it suggests one good next tile. On 3 × 3 it follows a shortest path; on big boards it is a helpful nudge rather than a perfect plan.