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You will need

• Set of dominoes
• Blu-tack
• Sticky labels, pens, scissors (optional)

What to do

The puzzle you have just made is a type of sliding block puzzle. These puzzles have been around for over one hundred years, and used to be very popular amusements before the invention of television. One of the most famous is called 15 and requires you to rearrange fifteen numbered blocks to put them in order. More modern sliding block puzzles have pieces of a picture on each block, and the goal is to re-create the whole picture.

The puzzle you just made is known as Hughes’ Puzzle. It has two dominoes missing from a full rectangle. To move the tall skinny piece sideways, you need to have both spaces one on top of the other, and to move the square pieces up or down, you’ll need to have the two spaces side by side.

Real-life maths

There are many strategies you can use to solve a sliding block puzzle. However, a trick that works on one sliding puzzle might not work on another. For some sliding block puzzles, the best way to find the answer might not be much better than just randomly sliding blocks until it has been solved.

Some mathematicians study how long it would take a computer to answer a question. They put each type of question into a category based on how hard it is. Sliding block puzzles are in the category PSPACE-complete, which is a very hard category. Sliding block puzzles take more time for a computer to solve than Sudoku, but they aren’t as hard as a game of chess.