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?
We received lots and lots of very
well-described solutions to this Teddy Bear problem - I'm sorry
that we can't mention everyone. It was interesting to see what you
called a 'move'. Jessica decided that a move was a 'swap':
Jessica says this is not a unique
solution, meaning that it can be done in four moves, but in
different ways. Will, Milly and Emily from Swiss Gardens Primary
School agreed with Jessica and sent in this picture of the four
moves they made, which are slightly different from
Gemma and Maggie, also from Swiss
Gardens, looked at simpler cases with smaller numbers of bears.
It can be useful to do this to see if
you can identify and explain the pattern. I wonder whether you
could predict the least number of moves for five lots of five
Jodie thought about a 'move' in a different
way and here is what she did:
Elijah also used this idea and, like Gemma and
Maggie, he investigated simpler cases. He even tried five lots of
five bears as well:
Fantastic reasoning, Elijah, thank you for
your detailed solution. We can really understand how you were
We also received the following message from a
mum which I couldn't resist including!