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?
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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 James':
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 words:
Alice from Henrietta Barnett and Patricia from Chongfu Primary School both described the six solutions too.
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!