NO. 01b / THE SMALLER SLIDE
8 Puzzle.
Room to learn.
A shorter row. A clearer view of the gap.
The 8 Puzzle makes every cycle visible.
THE 3×3 RULES
Read it like
three short lines.
The finished board reads 1, 2, 3 across the first row; 4, 5, 6 across the second; then 7, 8 and the empty space. Only a tile sharing an edge with the gap can move. A diagonal neighbor cannot slide, and two numbered tiles cannot exchange places directly.
Tap the tile, not the gap
On touch screens, tap an outlined tile beside the gap. With a keyboard, focus the board and press an arrow in the direction a numbered tile should travel. If the gap is at the bottom right, ArrowRight pulls the tile on its left into the gap. An illegal move leaves both the board and the move count alone.
Pause stops the clock and hides the board. Restart repeats your starting position; New puzzle reshuffles it. Undo reverses the last slide and adds one to the move count. Your 3×3 board is remembered separately from 4×4 in this tab, so switching sizes never replaces an unfinished 15 Puzzle.
A hint is a next step, not an automatic move
Hint highlights one neighboring tile from a route verified all the way to the finish. It may temporarily move a number away from home. The route is constructive, not a claim of the fewest possible moves. Showing a hint marks the attempt Assisted, including after undo or restarting that same shuffle. Solo and Assisted bests stay separate for all three difficulties.
WHY SIZE CHANGES THE TEST
For 3×3,
count the inversions.
Ignore the gap and read left to right. An inversion is a larger number appearing before a smaller one. On this odd-width board, a position is solvable exactly when that count is even. The gap’s row does not need to be added.
The example swaps only 7 and 8: one inversion, no solution. Our starts are made by legal moves, so this impossible arrangement never appears as a new game.
ONE INVERSION · UNREACHABLE
A STRATEGY FOR NINE CELLS
Protect one row.
Cycle the rest.
Finish the top edge before chasing 8
Bring 1 to the top-left corner, keeping a route for the gap beside it. To finish the row, treat 2 and 3 as a pair: stage 2 at the top right with 3 below it, then bring the gap to the top middle. Slide 2 left and 3 up. You now have a complete top row without trapping the last tile.
In the bottom two rows, work on the left column as a pair: 4 above 7. Keep the right-hand 2×2 area free to cycle 5, 6 and 8 into place. If you cannot move a target directly home, steer the gap around it first. One slide can improve distance while blocking the next useful cycle.
Three starts, one goal
Easy shuffles with ten legal slides and keeps tiles near home. Medium uses fifty slides and a higher minimum distance from the goal. Hard uses 180 shuffle slides with tiles more dispersed. Shuffle counts describe generation, not shortest solutions. Difficulty does not resize the board or change how tiles move.
When to try the larger board
When completing a paired edge feels deliberate, move to the 4×4 15 Puzzle. It adds another row to protect and a different parity calculation. The 15 Puzzle strategy guide expands the same pair-first idea with a worked diagram.
Small-board questions.
How does the daily puzzle work?
Everyone gets the same numbered board for each UTC date. A shared dated link opens that original puzzle, even on a later day. Your attempt stays on its starting date across midnight. Restart keeps any hint use, and the first completed result is saved on this browser separately from free-play records. No account or consecutive-day streak is needed.
What gets shared with my daily result?
Only the issue, date, edition, move count, active time, Solo or Assisted label, and a link to that puzzle. The moves and answer are not included. Copy the text, or use the system share sheet where available. If copying is blocked, the result appears as selectable text. Nothing is sent automatically.
Why doesn’t the gap’s row enter the 3×3 test?
A vertical slide crosses two numbered positions in reading order, preserving inversion parity. A horizontal slide crosses none. The solved 3×3 board has zero inversions, so every reachable position has an even count.
Can I compare 8 Puzzle and 15 Puzzle best scores?
They use different spaces and routes. Records are kept separately by size, difficulty and hint use. A score on this board never replaces a 4×4 record.