Copyright © University of Cambridge. All rights reserved.

## 'Cubes Here and There' printed from http://nrich.maths.org/

Alfie from Grenville Combined School send in this solution.

I think there are 32 solutions in cubes here and there.

My method is to write each solution using the letter 'r' as red and 'g' as green and made a picture with each combination.

Perhaps you could send us some of these pictures, Alfie? That would be very helpful.

Here is a very good solution that was sent in by Martin and William (with lots of help from Sebastian) from St Martin’s Ampleforth .Well done you three! This is what they wrote and drew:
First of all, we tried to make random shapes according to the rules.

Then we realised that it wasn’t working, so we tried making groups of bases. This was more successful so we started making the cubes on top. Once we had finished we had an answer of $39$. However we found that we had duplicated some of the shapes. We got rid of them and our final answer is......$35$, as you can see here.

It was great fun working out the answer to this excellent challenge.

Is this all that there are or can you find any more?