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?
Taylor and Jessica from Stourport Primary sent
this solution to the first part of the problem:
Thank you both. Not many of you tried to
find more than one solution, but James from Haytor View Primary
sent us two different chains, both of which are different from
Taylor and Jessica's:
Oliver, also from Haytor View Primary,
sent in two more solutions:
Jed, Jordan, Cameren, Ashley, Charlotte
and Lewis, who also go to Haytor View Primary sent in solutions
too. Here are their various ideas which are different to those
Jack and Charlie from Stourport Primary found
And here is what was sent by Devansh from
Delhi Public School, Vasant Vihar:
Do you think we have found all the ways?
How will we know?
Lucy, Jodie, Josef, Jack and Jordan from
Haytor View looked at the second part and decided that you can't
use them all because you run out of pieces to use.
Alistair was able to explain this second part
of the problem:
Each piece has to have a pair of the same colour next to it in
the line, except for the end and the start. Also each piece has to
have a pair of the same shape next to it in the line. To get the
longest line, there are exactly ten pieces in the line with two
left over. The ten pieces include four shape pairs plus two odd
shapes at the ends.
James from Haytor View found another way to do
Maybe you can find another way.