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?
Many of you solved this problem for three
pairs of socks. Katarina explained:
What good advice, thank you, Katarina. I agree
that checking your solution is very important as it's easy to make
a mistake in this problem.
Bafiar, Yunus and Alper (from Private
IRMAK Primary and Secondary School Maths Club, Istanbul, Turkey)
Lucy from Bishop Ramsey School, Priya from
Loughborough High School and Katarina all then went on to introduce
another pair of socks of a different colour. They each foundtwo
ways to mix up the socks this time. However, Bafiar, Yunus and
Alper found more:
I wonder if you can explain how we know we
have got all the different ways?