Divide a set of stones which weigh $1g, 2g, 3g....555g$ into $3$ equal parts

Question

I managed to prove it for $5, 6, 9$ and $15$ sets of stones.

Is there some way to prove by induction that every number divisible by $3$ can be divided in this manner?

Answer 1

HINT: Can you see how to obtain a solution for $n+6$ from a solution for $n$?