Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What is the greatest number of squares you can make by overlapping
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Excellent solutions to this problem were sent
in by William from All Saints, Carshalton and Ruth from Swanbourne
William says that the black circle could be a
sphere, hemisphere, cylinder or cone.
Ruth explains that the square could be a cube,
a cuboid on its end or a square-based pyramid.
The triangle could be a triangular prism,
tetrahedron, one side of any shaped pyramid or a cone according to
Finally, Ruth says that the rectangle could be
any kind of prism, a cylinder or a cuboid. William also
suggests it could be a rectangular based pyramid.
Stephen who is home educated also said that
the square could be a triangular prism (with the non-triangle bits
being squares) and in fact any prism with square faces.
Thomas and Nathan from Our Lady and St
Werburg; Ebony, Lucy and Carys from Eaton Park Primary
and Armitage Class from East Hoathly also sent in many
of the above suggestions.
Jonathan from King David High School wrote in
with some suggestions of items which could make the shadows:
This is another way to look at the problem -
thank you Jonathan.