Sliding puzzle

Legal moves and the direction of your controls

Click or tap a numbered tile sharing an edge with the blank to exchange their positions. A diagonal tile cannot enter the empty square. You cannot jump over a number, move a whole row in one action, or exchange two occupied squares directly. Look at the blank to identify your choices: two neighbors at a corner, usually three along an edge, and up to four inside the board. Moving the blank changes which tiles are available next.

When the board has keyboard focus, the arrow keys move the blank in the named direction. Pressing Left brings the empty square left and slides its left-hand neighbor right. This is worth checking with one deliberate key press at the beginning: thinking in terms of tile direction produces the opposite expectation. An arrow pointing beyond the outer edge cannot perform an exchange. For reliable execution, read the new position after each input before starting another part of your route.

Space pauses or resumes while you are using the board. Pausing hides the tile arrangement and stops the timer. Leaving the browser tab also pauses play; resume when you return. Completion requires every number in its target square and the blank in the bottom-right corner. A nearly sorted display is an intermediate position, so check the whole target rather than assuming the last few numbers will fall into place automatically.

Choose one working tile and prepare its path

Begin with a limited question: where is tile 1, and what path could take it toward the upper-left corner? Locate its destination, then identify the side on which the blank must arrive. To move a tile upward, put the blank above it. To move it rightward, put the blank to its right. The preparation may involve several other tiles before you can move your chosen number even once. Those preliminary exchanges are useful when they provide a clear next step.

Imagine your tile needs to go up but the blank is beside it. Sliding the tile sideways simply because it is available may send it away from the route you intended. Instead, trace a path for the blank around the tile through the unfinished area. Make sure that path stays open after the first exchange. The mistake to avoid is building a neat boundary that cuts the blank off from the side you will need for the following move.

A tile sitting in its correct square is not necessarily ready to be protected. Early in a puzzle, it may be there by chance and still obstruct another tile's passage. Protect an area when it is part of your construction and you have enough room left to continue. This distinction makes temporary disruption easier to judge. You are creating a stable solved region, rather than trying to increase the count of correct-looking tiles on every individual move.

Build the top row, leaving room for its last pair

Bring tile 1 into the upper-left corner, then work on tile 2 beside it. Use the lower rows to circulate the blank without crossing the completed part of the top row whenever a suitable route exists. Do not declare unrelated correct tiles untouchable at the same time. That removes working space before you have a reason to remove it, turning an otherwise flexible board into narrow corridors that are difficult to navigate.

Plan tiles 3 and 4 together. Securing tile 3 first and only then looking for tile 4 can trap the latter beneath its target with no convenient way to slide it upward. Keep the last two positions open while you stage the pair nearby. The second row can serve as a waiting area, and one tile may temporarily occupy the other's destination. Assess this staging by asking where the blank will be after the next exchange and which tile will then be able to enter.

There is no universal arrow sequence you can apply without checking the setup. A useful short rotation depends on the locations of both numbers and the blank. Picture a circuit inside the active rectangle: which of the pair moves first, which square becomes empty, and can the other number reach its target without disturbing 1 and 2? If you cannot answer those questions, reposition the pair instead of closing the row immediately. Three tidy numbers do not compensate for a blocked fourth.

Once the complete row reads 1, 2, 3, 4, verify that your remaining working pieces and blank lie below it. Treat the top row as the boundary of the next stage. This reduces the number of locations you need to follow. Occasionally reopening a boundary can repair an earlier mistake, but do it deliberately: identify the number you must release and the route that will restore the boundary afterward.

Work on the second row inside the remaining rectangle

Tiles 5 and 6 are the next individual targets. Move the blank around them within the three unfinished rows, using a lower route when crossing the top would disturb completed work. Repeatedly advancing a tile often means alternating two tasks: place the blank ahead of it, exchange, then circulate the blank ahead again. Look for a circulation route before committing to the first step, especially when the tile is near a side wall.

Tiles 7 and 8 form another finishing pair. With less vertical space available, their relative order matters more than their apparent closeness to the final squares. A pair parked nearby in an awkward order can need substantial rearrangement. A pair farther away but correctly prepared may enter smoothly. Leave maneuvering space next to the pair and decide where the blank should emerge once the row is completed.

After placing the second row, make a short checkpoint: 1 through 4 are intact, 5 through 8 are ordered, and the blank remains in the lower strip. This catches an accidental extra key press before you mistake its consequences for a final-stage strategy problem. Recovering an execution error immediately is usually easier than remembering which protected number moved after several more minutes of play.

Switch to vertical pairs for the two bottom rows

The remaining area has only two rows, so finishing the entire third row first can remove the space needed to organize the fourth. Change the unit of planning to a column pair. Prepare tile 9 above tile 13 in the leftmost column. Use the other columns to bring them into a workable relationship with the blank, then complete both together. Once the pair is correct, keep that column outside your future circuits.

Next prepare 10 above 14 in the second column. The same principle applies: the first number should not be treated as permanently fixed while its partner is still stranded. If closing one square traps the second number, reopen that pair and prepare both before protecting the column again. Progress comes from shrinking the active area while preserving useful routes, rather than shrinking it at the earliest possible moment.

The lower-right two-by-two corner will then contain 11, 12, 15, and the blank. With all surrounding tiles correct in a reachable arrangement, moving the blank around that corner's perimeter brings the remaining tiles into their final positions. Inspect the board after each step and stop when it matches the target. If an earlier number is no longer correct, fix that premise first. Repeating a corner circuit cannot repair a misplaced tile outside the corner.

Use hints to inspect a move and records to inspect a route

The optional hint highlights an adjacent move using Manhattan distance. It helps you inspect a local choice; it does not compute and display an entire shortest solution. A suggested exchange may reduce distance while doing little for your current pair. Before taking it, connect it to a purpose: clearing access to tile 6, keeping the top row protected, or placing the blank beside 7 and 8. A useful suggestion still needs interpretation within your plan.

Assisted attempts are identified separately and do not replace an unassisted personal best. The local record prefers fewer moves and uses time to break a tie in move count. Learn to finish with a coherent route before trying to execute faster. A measured attempt with fewer exchanges can improve the record even if it takes longer. The displayed numbers describe your play on this browser; they are not a public leaderboard or an independently verified comparison with other players.

Retry restores the same starting scramble, making it useful for testing a different decision at a particular stage. New puzzle starts a different arrangement. Compare attempts from the same beginning and note whether you used assistance. Otherwise, a lower time may simply reflect a different problem. Browser storage keeps the personal record locally, so another device or cleared site data may not show the same best. Treat the record as practice feedback rather than permanent account history.

Why a generated board can be solved

A new board starts at the target and makes ninety legal exchanges without immediately reversing the previous move. It is never presented already solved. Reversing that preparation would recover the target, so a solution exists. The shuffle length is not a minimum solution length: its path can include circuits and there may be shorter routes back.

Manhattan distance adds each numbered tile's horizontal and vertical separation from its destination. Princeton's assignment explains this lower bound; it is not a rule requiring every next move to reduce distance. MIT's course text uses invariants to explain why arbitrary arrangements can be unreachable. For this edition, legal-move generation already preserves solvability, so you can focus on the route rather than testing a parity condition before play.

Practice one decision at a time

Set a specific goal for an attempt. First learn legal neighbors and the arrow convention. Next try completing the top row without accidental exchanges. Later focus on the second-row pair or the lower column pairs. Small goals reveal what needs attention: perhaps you found the target square but forgot to put the blank on the right side, or perhaps you protected a tile before its partner was ready. Each observation suggests a concrete adjustment.

After finishing, retry the same scramble and examine one expensive detour. You might circulate the blank on the other side, prepare a finishing pair earlier, or avoid repeatedly entering and leaving the same area. Change one part of the route so you can judge its effect. Check total moves as well as time. A shorter route that currently requires thought can become smoother through careful repetition without changing its underlying decisions.

Use an input method you can control comfortably. With a keyboard, ensure the board has focus before pressing arrows or Space. With touch or a pointer, identify the adjacent tile before activating it. MDN documents the role of keyboard operation and visible focus in accessible controls. Your practical rhythm can be one input, one check, then the next decision. Improving at this puzzle means learning its spatial relationships and routes; the game does not measure clinical abilities or guarantee general memory improvement.