There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
Here is a set of shapes. For this problem we will call them
Each of these pieces is either a different colour or a different
shape from all the others.
These problems ask you to arrange the pieces in a line so that
you change either colour or shape in the next piece along. If we
start with a blue triangle the next shape has to be either another
triangle or another blue shape.
The first puzzle is to arrange all the shapes in such a line
starting with the blue triangle and ending with the red circle.
There are lots of different ways of doing it!
The second problem is to arrange the pieces in the same way,
starting with the blue triangle and ending with the red circle, but
to change first colour, then shape or vice-versa.
If you put a yellow triangle after the blue one and so change
the colour, next you must put another yellow piece and so change
You will not be able to use all the pieces in this way but the
problem is to see how many you can use.
Why do you think you cannot use all the pieces?
You might like to try using this interactivity.