Sliding tile puzzles for children: putting the picture back together

A picture cut into squares, one square missing, and the rule that tiles can only slide into the empty space: sliding tile puzzles look simple, but they're a wonderful workout for spatial thinking and planning. Every move changes where the gap is, so children quickly learn that they need to think a few moves ahead.

This post explains how to make a sliding puzzle at home, how to start with very small boards, and a strategy that helps children solve bigger ones without getting stuck.

How a sliding puzzle works

The board is a grid, for example 3 by 3.
All the squares but one have a tile; one square is empty.
On each move, you slide one tile that's next to the gap into the gap. No lifting, no jumping.
The goal is to arrange the tiles so they make the picture (or follow a set order).

Because only the tiles next to the gap can move, you're really moving the gap around the board. That's a helpful way to explain it to older children.

Make one from paper

Draw a grid of squares on a sheet of card: 2 by 2 for a first puzzle, 3 by 3 later.
Draw a simple picture across the whole grid on another card the same size, or use an old greeting card. Bold colours and big shapes work best.
Cut the picture into squares that match the grid.
Remove one square, usually the bottom-right one. That's your gap.

Children love making the picture themselves, and it helps them recognise where each piece belongs.

The tip that keeps it solvable

Here's something surprising: if you mix up the tiles by lifting them and putting them down at random, about half of the time the puzzle cannot be solved at all, however clever you are.

To avoid frustration, always mix up a sliding puzzle by sliding, starting from the finished picture. Make 10 or 20 random slides, and you know a solution exists, because you can always undo your slides. This is also a nice way for children to mix up a puzzle for you.

Start with small boards

2 by 2 (three tiles): the tiles just go round and round the board. Children around 4 or 5 can solve this and discover that the tiles move in a circle.
2 by 3 (five tiles): a real puzzle, but short. A good step for ages 6–7.
3 by 3 (eight tiles): the classic. Many children around 8 and older can solve it with a strategy and some patience.

Only move to a bigger board when the smaller one feels easy.

A row-by-row strategy

On a 3 by 3 board, trying to fix everything at once leads to going round in circles. A step-by-step plan works much better:

Solve the top row first, one tile at a time, working left to right.
Don't disturb the top row once it's done, if you can help it.
Then solve the left column of the two remaining rows.
Finish the last little 2 by 2 corner, where the tiles just go round in a circle.

The tricky moments come at the end of a row: sometimes the last tile can only get into place if you temporarily move a finished tile out of the way and put it back afterwards. Children often resist this at first, so talk about it: "Sometimes we have to undo a little to make progress." It's the same idea as bringing the goat back in the river crossing puzzle.

Tips for playing together

Talk about where the gap is: "If the gap goes here, which tile can move next?"
Count moves for older children and try to solve it in fewer moves next time.
Take turns making moves on the same puzzle and discuss each one.
Stop while it's fun. A half-solved puzzle can wait on the table until tomorrow.

In Dologi, "Slide the picture" puzzles cut a picture into tiles on boards from 2 by 2 up to 3 by 3, and children slide the tiles back into place, starting small and moving on to bigger boards as they grow more confident.

In short

In a sliding puzzle, you only slide tiles next to the gap into the gap.
Make one from card with a simple picture, starting with a 2 by 2 board.
Always mix up the tiles by sliding, never by lifting, so the puzzle stays solvable.
On bigger boards, solve row by row, and accept that sometimes you need to undo a little to move forward.