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.