Boyang from Mountfields Lodge and Caroline from St Jude's C of E School looked at this problem very logically. To balance 7 on the left using two "half" weights on the right, Boyang told us:


The two numbers on the right hand side could be:
1 2 + 6 1 2
1 1 2 + 5 1 2
2 1 2 + 4 1 2
3 1 2 + 3 1 2
4 1 2 + 2 1 2
5 1 2 + 1 1 2
and finally, 6 1 2 + 1 2 .

I wonder whether the first solution is different from the last one? What do you think?

Caroline wasn't sure whether you are allowed two weights on the same hook, but I think that's fine.

Nobody has looked at hanging three weights on the right-hand side, or having quarter divisions on the balance. If you do investigate these situations, let us know!Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.