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?
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?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Thank you for the solutions we received
for this problem. You agreed that there are six different ways of
building a house for seven people. Chris from Holyport C of E
Primary, Yasi from Canberra Grammar and James from St Woolos,
Newport all sent in pictures of the houses. Here is
I like the way
you have done this in a very logical order, James, moving one
'room' from the left to the right each time. Jordan
also wrote to us and described the same method as James', but in
Alice from Henrietta Barnett and Patricia
from Chongfu Primary School both described the six
However, Callum from Canberra Grammar
School went a step further and decided to look at different
combinations of rooms if they were different
colours. So, for example, you may decide
you have two red rooms, two yellow rooms and three blue rooms.
You could then investigate the number of different ways
you could arrange the coloured rooms for each of James' pictures.
This makes a nice extension to the problem,
Callum - well done!