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'Are You Well Balanced?' printed from https://nrich.maths.org/

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You might like to have a look at the activity Number Balance before trying this problem.

Here is an interactive number balance:

You can hang weights on the hooks. All the weights are exactly the same and you can hang more than one weight from each hook.
 
Take some time to have a play with the balance.
 
I hang one weight on the 10. I want to use just one hook on the other side to make it balance.
Where could I put weights and how many would I need to put on?
Is there only one solution?
How might you record your solutions so you don't forget them?
 
Now I hang two weights on one of the 10 hooks.
Using only the 2 hook, how could I add weights on the other side to make it balance?
Using only the 5 hook, how could I add weights on the other side to make it balance?
How could I make it balance using both the 2 and the 5 hooks? Is there only one solution?
Can you find all the solutions?
How do you know you have found them all?