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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:
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. Teachers - you might like to send a summary of your children's work.