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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?

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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?

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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?

3 Blocks Towers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

We had these good solutions sent in to this challenge. Jemima told us the order in which she worked to find all the solutions:

I used multilink cubes to make the towers. First of all, I looked for towers that were red at the top. Then I looked for towers that were yellow at the top. Then I looked for towers that were blue at the top. These are the ones I found.

Red, blue, yellowRed, yellow, blueYellow, red, blueYellow, blue, redBlue, red, yellowBlue, yellow, red

Then Jack from Gosforth Central Middle School explained very clearly why only six ways are possible:

With three different colour blocks there are six possible ways of building the tower. This is because for each colour on top there are two options for the other blocks. Therefore as there are three colours to go on top there are $3$ x $2$ options in total, that means six.

David worked systematically like Jemima had done, trying the problem with four blocks. Here are the towers he found:

Red, yellow, blue, greenRed, yellow, green, blueRed, blue, yellow, greenRed, blue, green, yellowRed, green, yellow, blueRed, green, blue, yellowYellow, red, blue, greenYellow, red, green, blueYellow, blue, red, greenYellow, blue, green, redYellow, green, red, blueYellow, green, blue, redBlue, red, yellow, greenBlue, red, green, yellowBlue, yellow, red, greenBlue, yellow, green, redBlue, green, red, yellowBlue, green, yellow, redGreen, red, yellow, blueGreen, red, blue, yellowGreen, yellow, red, blueGreen, yellow, blue, redGreen, blue, red, yellowGreen, blue, yellow, red

Well done these are excellent solutions showing how well you worked systematically.