Tangram puzzles online

The seven tangram pieces

A tangram is a square cut into seven pieces, called tans: two large triangles, a medium triangle, two small triangles, a square and a rhomboid. Every figure here uses all seven, with no gaps, no overlaps and nothing over the edge, and every one has been tiled by a solver before going up, so each can be done.

The puzzle comes from China, where it was printed in the late eighteenth century, and reached Europe and America in the 1810s as a craze. The large triangles are half the figure between them, which is why the classic advice is to place them first: they have the fewest places they can go.

How to play

Not sure where to start? How to play has the rules and the controls, and walks through a whole figure one piece at a time. If you would rather learn with the pieces in your hands, the interactive tutorial solves the square with you.

How difficulty is rated

There are four difficulties, each with the tag it wears on the shelf and over the board:

• Difficulty: easyThe outline gives most of the pieces away.
• Difficulty: mediumSome of the pieces have to be worked out.
• Difficulty: hardThe outline gives almost nothing away.
• Difficulty: impossibleOnly the variations, with pieces of their own and one plain shape to fill.

Every tangram puzzle is rated easy, medium or hard, and the rating is measured from the shape rather than guessed. What makes a tangram hard is how little its outline gives away: a piece with its edges on the outside of the figure shows where it goes, while a piece hemmed in by other pieces has to be worked out.

To rate a puzzle, we add up the length of piece edge hidden inside the figure, where one piece meets another and the silhouette shows nothing. The more of it there is, the harder the puzzle. That is why a figure with parts sticking out is usually easy, and a plain square, which looks the simplest of all, is among the hardest. We checked the measure against how long people take over their first solve of each puzzle, and it holds.