Rule : All the while you can only have one weight at each
numeral on the balance.
Let's start by saying that on one side of the balance, place two
weights and keep them there. Make it balance by placing $3$ weights
on the other side (remember only one at each numeral!).
So you might start with an $8$ and a $3$ on one side, and find you
have to have something like these for it to balance:
So choose your two places on one side and find many different
balance places on the other side.
When you've done all you can, it might be an idea to choose
another (maybe higher) pair of numbers for one side and find all
the ways of placing $3$ weights on the other side.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.