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Penta Place

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

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Tetrafit

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Shapely Tiling

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Amanda from Wallace Hall Academy has sent us a solution to the first part of the question:

You make a regular octagon by making the outline of it with triangles. To do this, you make one quarter of the pattern (i.e. a quarter of the whole interactivity image) orange, so there is an orange square. Then you make the smaller triangles on the edges purple. Then you make the central octagon white, and you will have an octagon outlined by orange big triangles and purple small triangles.

Here is a picture of Amanda's octagon and triangles, using just one quarter of the pattern:

white octagon surrounded by small purple triangles and larger orange triangles

Ling from Beecroft Primary School, Australia has found a way of producing irregular hexagons with triangles and squares. Here is the image she sent:

irregualr hexagons, triangles and squares tessellation
Let us know if you find any others.