15 Puzzle Rules and How to Solve It

A four-by-four board holds sixteen spaces. Fifteen tiles numbered 1 through 15 sit on it and one space is left blank. You slide a neighboring tile into that blank space, over and over, until the tiles read in order. You never lift a tile out or jump it over another, and none ever leaves the board. That single sliding motion is why it is called a sliding puzzle.

This form became widely known around 1880, spreading fast across the United States and Europe. A famous stunt at the time swapped only tiles 14 and 15 and offered a prize to whoever could restore the order, but that particular arrangement can never be solved no matter how you slide it. Mathematicians soon proved why, and the puzzle has stood ever since as both a toy and a textbook example of permutation parity.

Here is the core fact. Swap any two tiles just once and the new arrangement belongs to a different half of all possible layouts than the original. A sliding move can never cross that line, so if you pick tiles up by hand and set them down at random, about half the time you get a board that can never be solved. That property is called the parity of a permutation, and it is exactly why how a board gets built matters so much.

What the board looks like

Four columns, four rows. Fifteen of the sixteen spaces hold a tile and one is empty. Think of the blank space less as a missing tile and more as your workspace, since it is the only thing that ever moves. In practice you are dragging the blank around the board rather than the tiles themselves.

How a slide works

Only a tile directly above, below, or beside the blank space can move. Press it and it slides into the blank, leaving a new blank where it used to be. No diagonal moves, and never two spaces at once. So every move is really one tile and the blank trading places.

When you are done

The top row reads 1, 2, 3, 4 left to right, the next row 5 through 8, then 9 through 12, then 13, 14, 15, with the blank left in the bottom right corner. There is no move limit and no clock, so you can bring any tile home first, but as the technique sections below show, working in a fixed order is far faster.

From here on this is what this particular app actually does. Every 15 puzzle shares the rules above, but the details differ from app to app, so it helps to read this once.

One board a day, the same for everyone

The board is built by folding today's date into a single number. Everyone who opens the app on the same day gets the same board, and a new one opens when the date changes. The date comes from your device's local clock, so if you leave the page open past midnight you need to reload to see the next board. Both building and solving happen entirely in your browser, so there is nothing sent to a server and no account is needed.

Every board is solvable, always

Because of the parity fact above, laying tiles down at random would leave you with an unsolvable board about half the time. This app does not check for that risk after the fact and reject bad boards, it makes sure the risk never exists at all. It starts from the finished, solved state and applies one hundred twenty real, valid slides to get today's board. Since it only ever walked away from the solution using legal moves, retracing that same path backward always leads home.

While shuffling, it skips any move that would immediately undo the one before it, since sliding back and forth cancels out and leaves the board less mixed. An automated check backs this up too, generating a hundred seeds and confirming each resulting board is solvable by parity.

How the move count works

The number in the top left is how many times the board actually changed. Pressing a tile that is not next to the blank does nothing, and the count does not move either, so a miss never gets counted against you, but sliding a tile out and right back in counts as two moves. A tile you can slide is shown on a white background, the rest sit in dimmer gray, so it's easy to see at a glance where you can press.

What is missing

Worth saying plainly what is not here. No hint tells you the next move, there is no single-step undo, and nothing solves the board for you automatically. It does not time you or tell you the minimum number of moves for a given board. There is also no saved progress. Reloading the page or closing and reopening it restarts today's same board from scratch with the move count back at zero. Keep that in mind if you plan to step away partway through.

Finishing and sharing

The moment all fifteen tiles land in place, your move count appears along with a share button, and the tiles lock so nothing slides anymore. Pressing the share text copies a short line with the date and your move count, or just says in progress if you copy before finishing. It never includes where any tile sits, so sending it to someone still solving does not spoil their board.

Everything below is something a person does by hand and eye. The app will not do it for you, but once it clicks it carries over to any sliding puzzle.

Watch the blank, not the tile

This is where beginners and experienced players split. Staring at the tile you want to move tends to freeze your hand, but deciding which side of that tile the blank needs to reach makes the path obvious. To send a tile one space right, the blank has to arrive on its right side, and steering the blank there without stepping on a row you already fixed is the whole trick of a single move.

Lock rows from the top, one at a time

Set 1 through 4 in the top row and never touch that row again. Then set 5 through 8 in the second row, which shrinks the remaining puzzle to two rows of four. The smaller the board gets, the less room the blank has to maneuver, so finishing the roomier top rows first while you have the space pays off. Within a row, fill left to right.

Place the last two tiles in a row together

In the first row, 1 and 2 slide in easily, but if you seat 3 in its final spot first, it blocks the path for 4 and you end up having to pull 3 back out. So handle the last two as one unit. Put 3 in the far right spot of that row and 4 directly below it, then bring the blank to the left of 3. Now sliding 3 left one space and 4 up one space drops both into place at once. The same move handles 7 and 8 in the second row.

Once the top two rows are locked, you are down to two rows, and sticking with the same approach here just makes you circle the same spot. There is no undo, so it pays to picture the slide in your head before you press.

Treat the last two rows as columns

Instead of seeing the remaining eight spaces as two rows, see them as four vertical pairs. Place 9 and 13 together in the left column, then 10 and 14 in the next, and so on. The method is the same last-two-together move from before, just rotated ninety degrees. Set 9 in the bottom left corner and 13 to its right, bring the blank above 9, then slide 9 up and 13 left, and both land together.

The last four are pure rotation

Once the vertical pairs are locked, you're left with two columns of two in the bottom right, meaning three tiles and one blank space. At that point there is effectively no other choice, only rotating those four spaces clockwise or counterclockwise. Turn one way a few times, and if the order comes out wrong, turn the other way instead. Since this board is always built to be solvable, if the first twelve tiles are truly correct, the remaining three are guaranteed to fall into place through rotation alone.

Cutting down your move count

The biggest source of wasted moves is the blank wandering for no reason. If the blank has to circle most of the board just to move one tile one space, that alone burns several moves. So plan not just your next tile but the one after it, aiming to land the first tile so the blank stops somewhere useful for the second. Set up the direction you are driving your target tile against the direction the blank naturally travels, and the back-and-forth drops noticeably.

A locked row keeps breaking

Steering the blank upward to fetch the next tile and running it straight through a finished row scrambles that row again. Treat any locked row as off limits and route the blank below or around it instead. If you slip and nudge a locked tile by accident, undo it right away. Without an undo button, the longer you wait the harder it is to trace back where things went wrong.

The last two in a row block each other

This is the most common jam. If you seat one of the final two tiles in its spot first and then try to slide the other one in, it forces the first one back out every time. Don't hold onto it out of stubbornness, deliberately pull the seated tile back out and rebuild the vertical setup described earlier. Going back to that paired slide is, in the end, the fastest way through.

The last three just keep spinning

If the final three tiles are only out of order and keep cycling, try turning the other direction. If that still doesn't line them up, the problem probably is not the last three at all, it's likely that one tile you thought was already locked earlier is actually in the wrong spot. Scan the board from the top left by number once to check. You do not need to worry about the board itself being unsolvable.

Your progress disappeared

If reloading sent the board back to the start, that's not a bug, it's simply that there is no save feature. Today's board comes from the date, so the same layout opens again. Start when you have time to see it through, and if you do need to step away, leaving the tab open is your best bet. A new board opens once the date changes.