### Homes

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

### Stairs

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.

### 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?

# Name the Children

## Name the Children

Eight children from Blue Class were ready for games early. Their names, in alphabetical order, were Ali, Baxter, Chris, Danny, Ella, Fred, Greta and Helen. They stood (not in alphabetical order) by the edge of the field watching Red Class playing football.
Can you name the children using the five clues below?

1. Ella and Fred have fair hair.
2. Ali, Baxter and Greta have black hair.
3. Ali, Chris, Danny, Ella and Fred all have special red shirts for games.
4. Baxter and Ella are taller than the others.
5. Ali, Chris and Helen are shorter than the others.

### Why do this problem?

The idea of this problem is for children to adopt a systematic approach to the order in which they can use the information. They will need to prioritise the clues which immediately help them to name a child and then move on to the clues which are perhaps more ambiguous, gradually narrowing down the options.

As the hints suggest, having a way to record their thinking will be vital. This photocopiable sheet might be useful.

### Key questions

How are you going to record what you have done?
Why don't you could call the children by the first letter of their names - A, B, C etc?
What about sketching out the line of children?
Why don't you write all the possible letters by each child until you have found out exactly who each one is?

### Possible extension

Learners who found this easy could try Rabbits in the Pen.

### Possible support

Suggest using this sheet to jot down possibilities or start with this similar, but easier problem, Whose Face?