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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

Some people have noticed that the sums of the angles in a hexagon add up to 720 degrees, and so the sum of the other three angles must be 360 degrees as well. We know that the two equal sides must be parallel because there are 360 degrees between them. So we may tessellate the hexagons as shown. (Look for diagonal lines from top left to bottom right. Each line consists of hexagons in the same orientation, but the lines alternate.) It is easy to check that the angles at each vertex do indeed sum to 360 degrees; this also follows from the condition given because A+B+C and D+E+F are each 360 degrees.