### Homes

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?

### Train Carriages

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?

### Let's Investigate Triangles

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?

# We'll Bang the Drum

##### Stage: 1 Challenge Level:

Genia from Deer Park School thought hard about this problem:

For this problem there are 3 possibilites to put two drums on the wheel with 6 circles on it.
One of them is putting 2 drums on first and second circles.
The second one is putting 2 drums on first and third circles.
And the last one is putting 2 drums on second and fifth circles.
But there are also three speeds. So we will take all three of our rhythms and multiply it by three different speeds = nine (that's how many rhythms you can make with just two drums and a wheel with six circles on it)

Well done, Genia. Perhaps you have described your ways slightly differently to Genia but you should find if you are looking for DIFFERENT possibilities, then there are only three. Matt from Lincoln looked at having three drums on the wheel. He says:

I simply put a drum in one spot and kept it there while I changed the position of the second. Then after I figured out all of the solutions for one being in that spot I moved the first one over and repeated the process. However, I took care not to repeat the same rhythms.

You've described a very good way of approaching the problem, Matt. It's good to have some sort of system for finding all the ways so that you can check whether you've got them all. Matt thinks there are 15 different ways, but unfortunately you didn't say what they are, Matt. Perhaps you coud list them for us? Does anyone agree or disagree?