# Can you solve this problem?

Take a cube and surround it by a ring of other cubes that MUST touch two others. How many cubes do you need to do this?

Imagine surrounding this ring with more cubes.
How many more cubes are needed now?
How many cubes will there be altogether?

Were you right?

What about a bigger ring? And another? And another?

How many cubes will there be in the 9th ring?
How many do you think there will be in the 100th ring?
How would you predict how many cubes there will be in any ring?

Thanks to Nrich for this problem.

1. aiden says:

Mr Sloan I agree with Sharon As soon as I got home I researched and found the Bouzouki.

2. Sharon says:

Mr.Sloan, this comment has nothing to do with maths but I have found out an instrument that might have been played in that Scottish Gaelic song. It is called the Bouzouki which is used mostly for Irish Folk music! I hope I am right as I am the first person to research this question!

3. issa says:

Mr Sloan, me, Hazy, Leyla,and Aycan thought you need to square the odd numbers(e.g) 3×3=9 5×5=25 7×7=49 and those are the answers we got.

4. Amina says:

Mr Sloan, me and Charlene think we’ve got the answer! We think; because you need eight cubes to go around the cube and sixteen to go around that with 25 going around that. We think you have to add seven to one (for the first surrounding) then for the second you add nine (so you need nine more cubes), the third you add ten more and so on… Mr Sloan please tell us if we are right! This was really challenging and we kept on changing our ideas. However, finally, we got there! (We think!).