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A triomino is a flat L shape made from 3 square tiles. A chess board is marked into squares the same size as the tiles and just one square, anywhere on the board, is coloured red. Can you cover the board with trionimoes so that only the square is exposed?

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Paving Paths

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

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LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Bow Tie

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
Thanks to Hannah, Sophie Rebecca of the Roos C.E Primary School, who sent in the beginnings of a solution but there is still much to do. I have added some comments below.

Firstly, we decided that we should use the rightangles on the shape to create a 360 degree pattern. We found that the pattern made a shape of a butterfly. We also found out that the butterfly pattern could be joined together.


Basic unit

What transformations of the original tile were needed to create this unit?
How do these basic units fit together to tessellate the plane?
What other transformations of the original tile are needed to cover the plane?