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## 'Weighted Numbers' printed from http://nrich.maths.org/

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Here is a balance. It has a hook on each end from which you can
hang weights.

My weights are numbers - I have $1$s, $2$s, $3$s, $4$s, $5$s, $6$s,
$7$s, $8$s, $9$s and $10$s.

If I put a $2$ on one side and two $1$s on the other side, it is
balanced.

If I put a $3$ on one side, I would need three $1$s to make it
balance. How else could I make it balance with just a $3$ on one
side?

If I had a $3$ and a $4$ on one side and three $2$s on the other
side, what do I need to add to make it balance and where?

I hang a $10$ on one side. How many different ways can you find of
hanging numbers on the other side to make it balance?