The scale MUST be a balance, but it CAN’T be a balance.
If you can only use known weights to determine an unknown weight, it can only be a balance; otherwise it could report an arbitrary weight.
But a BALANCE COULD measure the 5 2 1 6 case: 5+1 exactly balances 6.
If you MUST attach a story to a problem, please make it MATCH the problem.
There was another problem (whose number I don’t remember, but it’s difficulty was over 990) in which I could make no sense of the story. I would suggest (request) dispensing with the stories and using more worked-through examples.