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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'?

Schlafli Tessellations

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

Although the three regular tessellation (using squares, triangles and hexagons) are well known, they do pose a demanding challenge in terms of 'elegant' LOGO procedures.

This problem considers the eight semi-regular tessellations, which geometrically are more stimulating and are shown below, along with their respective Schlafli symbols.

Look carefully at each diagram in turn. What is the meaning of the symbols?

The symbols are used in two and in three dimensions in classifying the regular and semi-regular solids. You can see an account of this in this NRICH article by Warwick Evans.

Can you construct some elegant procedures to replicate these images?