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'?
Students from Cowbridge Comprehensive School
in Wales took a look at this problem. They convinced themselves
that there are only 3 regular polygons that can be used to create
regular tessellations. Some used this spreadsheet to
justify their conclusion.
Catherine, from St. Michael's School, explained why it is possible
to produce a semi-regular tessellation with triangle, hexagon,
triangle, hexagon (or 3,6,3,6) meeting at each point:
She then offered another semi-regular
You can use the interactivity provided with
the problem to check that this combination works.