Solve it in layers, never all at once
Trying to nudge every tile towards its home at the same time is why the puzzle feels hopeless. The method that always works is to finish the top row completely, then the second row, and never disturb them again — after two rows the remaining problem is a 2x4 area, which is small enough to solve by feel.
Within a row, place the leftmost tiles first and save the last two for a single combined move. Putting tile 3 and tile 4 in place one at a time is impossible without breaking one of them — instead park 4 directly under its target, slide 3 into the corner, then rotate both into place together.
Why every shuffle here is solvable
Exactly half of all possible arrangements of a 15 puzzle cannot be reached from the solved state, no matter how long you slide. Swapping just two tiles in a finished puzzle produces one of these — a board that looks completely normal and is provably impossible. The property that separates the two halves is a parity count of how many pairs are out of order, combined with which row the blank sits in.
Every board on this page is shuffled by sliding tiles backwards from the solved position, so it always lands in the reachable half. If you are stuck, the arrangement is not the problem.
The puzzle owes its fame to exactly this fact. In the 1880s a prize was offered for solving a board with the 14 and 15 swapped, and the resulting craze sold enormous numbers of an impossible puzzle.
Cutting your time down
- Use the arrow keys. Keyboard slides are far faster than aiming at small tiles, and the timer only starts on your first move.
- Plan the blank's route, not the tile's. Every tile move is really the blank walking around to the far side of the tile you want to shift.
- Finish the bottom-left tile of the last two rows before the bottom-right — the final column resolves itself once the left is fixed.
- Do not restart because a row broke. Rebuilding one row costs a few seconds; a new shuffle costs the whole solve.
Frequently asked questions
Can a shuffle ever be unsolvable?
No. Half of all random tile arrangements are mathematically unsolvable, so this game never places tiles at random — it starts from the solved board and slides tiles backwards hundreds of times. Anything reached by legal moves can always be solved by legal moves.
Any tips for solving faster?
Solve row by row: finish the top row first, then the next, without breaking completed rows. For the last two rows, work column by column from the left, placing the two tiles of each column together. The final 2×2 corner then resolves with a simple rotation.
What is a good time for the 4×4?
Casual players typically finish a 4×4 in 2–5 minutes. Under a minute is genuinely fast, and speedsolvers who practice finger tricks can go under 30 seconds. Beating your own best time is the most satisfying benchmark.
Who invented the 15 puzzle?
The craze began around 1880, and the invention is generally credited to Noyes Chapman, a New York postmaster. Puzzle showman Sam Loyd later claimed it and famously offered $1,000 for solving a version with tiles 14 and 15 swapped — a prize that was safe forever, because that arrangement is mathematically impossible.
How many moves does a perfect solution take?
For the classic 4×4, the hardest positions need exactly 80 single-tile moves — the puzzle's so-called God's number, proven by computer search. Most shuffles need fewer, and human solvers typically use far more, since move-efficient solving means planning several tiles at once instead of fixing one at a time.
Why is the 5×5 so much harder than the 3×3?
Every size jump multiplies the possibilities enormously: the 3×3 has 181,440 reachable positions, the 4×4 over ten trillion, and the 5×5 vastly more still. Bigger boards also mean longer solutions and more completed rows to protect while you work, so patience and a solid row-by-row method matter far more.