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