### 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?

### 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

##### Stage: 1 Challenge Level:

Many of you sent in your answer to this problem, but very few of you told us how you did the problem. Remember, it is important to tell us what you did to solve the challenge so that someone else could follow it if they were stuck. Georgie C from St George's School did send us details:

I started by writing down all the features the anonymous children had (i.e child 1 has black hair and a green top) and wrote down all the possible names each child could have.
The first clue said that Ella and Fred had fair hair. I crossed off the names Ella and Fred leaving me with 2 fair headed children who were going to be Fred and Ella. As one is a girl's name and another a boy's, it was easy to tell which name belonged to who.
Next, it said Ali, Baxter and Greta have black hair meaning that the 3 black haired children were Ali, Baxter and Greta but you don't know which is which.
The next clue tells us that Ali, Chris and Danny have red game shirts. We have already worked out who Ella and Fred are, leaving us with Ali, Chris and Danny. In the previous clue it said that Ali was a child with black hair and as there is only one child with a red t-shirt and black hair, this must be Ali.
In the fourth clue it tells us that Baxter and Ella are taller than the others. We know who Ella is, leaving Baxter to be the other person which then means Greta is the one with black hair at the start of the line.
The final clue says that Ali, Chris and Helen are smaller than the rest. We know who Ali is, leaving Chris and Helen. It said earlier that Chris wore a red t-shirt leaving the other small person to be Helen.
Finally, Chris has to be the smaller one out of him and Danny leaving you with the following line up:

GRETA CHRIS BAXTER DANNY ALI FRED ELLA HELEN

Well done, Georgie. Well explained solutions were also sent in by Azure from Hanoi International School and Plum from Ardingly College Junior School.