## Tangram

### Rules

Pieces

Tangram is a puzzle made of seven flat shapes: five triangles, a square and a parallelogram. The triangles are isosceles and right-angled and they come in three different sizes: two large, one medium and two small ones. The parallelogram's acute angles measure $$\frac{\pi}{4}$$ and the smallest side has the same length as the square's side.

Taking as an area unit the square's area, the pieces have the following areas:

• area 2: large triangles
• area 1: square, parallelogram, medium triangle
• area $$\frac{1}{2}$$: small triangles

Goal

Given an image, the goal is to build a similar figure using all (and only) the puzzle pieces, without overlapping.

We'll call the given image the shadow image, where the inner borders of the built figure are not shown. The image where the inner borders are displayed is the solution image.

Examples of constructions that are not allowed:

Because all the pieces would have to be used, and the three pieces on the bottom weren't.

Traditionally, it is required that the pieces are interlocked in such a way that, considering any two pieces A and B, there is a sequence of pieces from A to B in which any two consecutive pieces touch each other. This rule is important to create shadow images, but not for solving the puzzle that is already built upon a certain image. In any case, this tells us that, if we wish to follow the traditional rules, every shadow image must be connected.