Sliding puzzles look like chaos until you learn to shrink them. Here is the method our studio swears by, explained without any maths.
First, stop trying to solve the whole board
The most common mistake with a sliding puzzle is treating it as one enormous problem. People push tiles around hopefully, a promising patch appears, and then three moves later it falls apart again. The board feels slippery, as if it is resisting you, and frustration arrives quickly.
The fix is to solve the puzzle in layers. You finish the top row and then never touch it again. You finish the left column and never touch that either. Each time, the part you still have to think about gets smaller, until you are left with a little 2x3 or 2x2 corner that almost solves itself. Breaking the job down like this also makes it far easier to pause halfway and come back later, because you always know which layer you were working on.
This works on every size, from a 3x3 on a short bus ride to a 5x5 that fills an afternoon. A 5x5 becomes a 4x4 once you finish a row and a column, and a 4x4 becomes a 3x3 the same way. In other words, if you can do the smallest board, you already know how to do the biggest.
Placing a row, and the trick for its last two tiles
Start with the top-left tile. Walk it to its home by moving the gap around it, rather than dragging the tile directly, then do the same for the next tile along. For most of the row this is relaxed work, because there is plenty of room below to manoeuvre.
The last two tiles of a row are where people get stuck, because placing one usually knocks the other out. The answer is to treat them as a pair. Park the final tile directly below its home corner, put the second-to-last tile in the corner itself, then slide them in together with a short loop of moves.
It feels odd the first time, a bit like stepping back to go forwards. After a couple of tries it becomes muscle memory. If you get muddled, simply undo the half-placed pair by moving those tiles down out of the way, and set them up again. Nothing you have finished above is at risk. The same pairing trick returns for every row and column you build, so learning it once pays off again and again on every board size.
Columns, then the shrinking puzzle
With the top row done, turn to the left column and use exactly the same idea, only standing on its side. Place tiles from the top downwards, and when you reach the last two in the column, park them as a pair and slip them in together.
Now look at what is left. On a 3x3 you have a 2x3 block; on a 4x4 you have a 3x3; on a 5x5 you have a 4x4. Repeat the row-then-column routine on that smaller board. It is the same handful of moves over and over, which is why experienced players can finish surprisingly quickly.
Keep an eye on the gap while you work. If it wanders into the solved area, you will have to disturb finished tiles to get it out. A good habit is to bring the gap back towards the unsolved region after every placement, so it is always where the action is. A gap parked in the right spot can save a dozen moves on a big board.
The final corner and why it always works out
Eventually you reach a 2x2 or 2x3 patch. This is the part beginners dread, but it is the easiest of all. Rotate the remaining tiles around the gap in a little circle, like a slow carousel, until each one lines up with its spot. Watch one tile at a time rather than all of them at once.
Some puzzles you find around the place are generated carelessly and can genuinely be impossible, with two tiles swapped forever. A properly made puzzle starts from the finished picture and is scrambled with real moves, so a route home always exists. Strata Shuffle works that way, which means a stubborn corner is never a dead end.
If the final rotation seems to go round and round without settling, check the row above. Very often a tile there is a single step out of place, and the corner is trying to compensate. Fix the row, and the last corner will fall in neatly. Patience at this stage is usually rewarded within a handful of moves.
Pictures, numbers and getting faster
Picture puzzles add a lovely extra layer, because you are reading the painting as well as the grid. Distinct features, such as a waterfall, a skeleton in the cliff or a bright volcano, are easy to place. Big areas of sky or sea are the hard part, and that is when a numbers overlay earns its keep.
There is no shame in switching numbers on for a 5x5. Plenty of players use them the first time through a picture and then turn them off on a repeat, when the painting itself has become familiar. Peeking at the finished image now and then is just as sensible. The aim is to enjoy the picture coming together, not to prove anything to anyone.
Once the method is second nature, the game becomes about thrift. Count your moves, notice where you wandered, and try the same picture again. Shaving twenty moves off a 4x4 is a deeply satisfying thing to do with a cup of tea on a quiet British evening, and the stars will tell you how far you have come.