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Triominoes

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'?

Tessellating Hexagons

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If three adjacent angles add up to 360 degrees, what do the other three angles add up to?

The shape given in the problem does tessellate. Call the unmarked angles D, E and F and label the angles of the polygons accordingly in the tessellation. What do you notice?

Draw some different hexagons that satisfy the criteria and see what happens. It may be best to work on square and/or isometric dotty paper so that the angles can be worked out accurately and the tessellations drawn easily.