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?

Jumping Cricket

Stage: 1 Challenge Level:

Harry sent us his thoughts on this problem:

My first way was that El Crico jumps along one tile, down three tiles and along one tile.

Then I thought that there are six different ways El Crico starts off his journey. He jumps along one, two or three tiles or he jumps down one, two or three tiles. Then he has two moves to get to the end. One of these jumps takes him to the very right of the board and the other takes him to the very bottom.

I made a table of all the possible moves. There are twelve of them.

 First Move Second Move Third Move Along one Along two Down three Along one Down three Along two Along two Along one Down three Along two Down three Along one Along three Down one Down two Along three Down two Down one Down one Down two Along three Down one Along three Down two Down two Down one Along three Down two Along three Down one Down three Along one Along two Down three Along two Along one

That's great, Harry. Thank you!