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'?
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.