Thank you to everyone who sent in their ideas about how to make the scales balance.

Amy from Stoke by Nayland Middle School sent us her work on this problem:

On the first question you would need to put a weight on number 2 on the right side.

On the second question you would need to put a weight on number 7 on the left side.

On the third question you could put one weight on 1 on the left side and the other on 2 on the right side.

Well done Amy!

Sam from Shepherd School noticed that there were several answers for the third question:

You could put them on point 6 on the right and point 5 on the left, for example. There are 9 solutions to this, they could go anywhere where the weight on the right is 1 more than the weight on the left.

Thank you for that clear explanation, Sam.

Saif from Pierrepont Gamston Primary School in England also found several solutions to the third question:

To balance the third set of scales you can have 9 possibilities which add one weight to the following columns:
1 left and 2 right
2 left and 3 right
3 left and 4 right
4 left and 5 right
5 left and 6 right
6 left and 7 right
7 left and 8 right
8 left and 9 right
9 left and 10 right

Well done Saif! How has Saif made sure that they have found all the possible solutions?