### 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.

### 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?

# Four Colours

##### Stage: 1 Challenge Level:

Children at Underhill Junior School coped well with this problem when we went in to use the NRICH site with them. Many were able to explain how they had done it very clearly. Among these were Adam & Kane, Rochelle & Matthew and William & Anthony.

Rochelle and Matthew said:

You make two "faces" with one of each colour -

Put one of the "faces" down and lay the other on top but twisted half way:

Adam, Kane, William and Anthony added that cubes the same colour must be diagonal to each other.

Pupils from Moorfield Junior School used triangular paper to draw their solutions, which worked very well. This is Emma and Abi's:

Their explanations were very similar to the ones above.