Number Balance

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?