What is a tangram?

A tangram is a square cut into seven pieces: two big triangles, one middle triangle, two small triangles, a square and a parallelogram. The puzzle is to use all seven to make a shape, usually shown only as a dark outline. You may not overlap the pieces, and every piece must be used.

The pieces are related in a neat way. Two small triangles cover the same area as the square, the middle triangle or the parallelogram. Two of those make one big triangle. Once you see that, you start to spot where each piece can go.

Why this version

Tangram Garden has 52 shapes in four chapters: people in action, animals, everyday things, and a chapter of Singapore shapes such as an HDB block, a kopi cup, a durian, a trishaw and a lion fish. The first shapes in each chapter draw the lines between the pieces, so younger players can match them one by one. Later shapes draw only the two big triangles, and the last ones show the outline alone.

The game does not check your answer against a fixed picture. It checks whether the pieces cover the shape. Many tangram shapes can be filled in more than one way, and any of them counts. There is also a daily shape, which changes at midnight Singapore time and always comes without lines.

A short history of the tangram

The tangram comes from China. In Chinese it is called qiqiao ban, often translated as the seven boards of skill. Little is known about exactly when or by whom it was invented. Historians think it appeared in the late 1700s or around 1800. The oldest tangram book that survives was published in China in 1813.

Sets and books reached Europe and America on merchant ships trading with Canton in the early 1800s. In 1817 tangram books were printed in London and Paris, and copies soon followed in other countries. For a few years it was a craze. Cartoonists of the time joked about people so busy with the puzzle that they forgot to sleep or work. The English word “tangram” came later, and nobody is sure where it comes from.

You may read that the tangram is 4,000 years old, or that it was invented by a man called Tan. Both claims come from a joke. In 1903 the American puzzle maker Sam Loyd published a book that gave the puzzle a made-up ancient history, with a god named Tan. By 1910 experts had pointed out that there is no trace of Tan or his books in Chinese writing. The real tangram is a little over 200 years old, which is old enough.

Mathematicians have played with it too. In 1942 two mathematicians, Fu Traing Wang and Chuan-Chih Hsiung, proved that the seven pieces can make exactly 13 convex shapes, the ones with no dents. The square you started with is one of them.

How to play

• Drag a piece from the tray onto the shape. It snaps into place when a corner or an edge is close.
• Tap a piece to turn it by 45 degrees. The Turn button turns the last piece you touched the other way.
• The parallelogram is the only piece that changes when you flip it over. Use the Flip button when it will not fit.
• Fill the whole shape with all seven pieces and no overlaps.
• Stars: one for filling the shape, one for using no hints, and one for finishing within the move aim. Each drag, turn and flip is one move.

Tips

Big triangles first. They cover half the shape between them, so they only fit in the widest parts. Place them early and the rest gets easier.

Look at the corners. A sharp 45 degree point can only be filled by the corner of a triangle or the parallelogram. A square corner can take a triangle’s right angle or the square.

Use spare pairs. If the square will not fit, two small triangles can often make the same patch, and the square can go somewhere else.

Try paper too. A square of card cut along the lines makes a set that fits in a pocket.

Your turn

Start with the standing figure, lines and all. By the end of the Singapore chapter you will be filling a shophouse from its outline alone.