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## 'A City of Towers' printed from http://nrich.maths.org/

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:

I started with seven cubes because I had to house seven
people.

I drew one stack and reversed it, just moving the odd cube across.

I used the same method two more times, changing the height of the
stack and moving it from left to right.

My answer is six different types of house.

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!