Eight Balls, One Heavy

Each weighing has three outcomes: left heavy, right heavy, balance.

$k$ weighings can separate at most $3^k$ cases.

1. 1. Lower bound

   One weighing distinguishes only $3<8$ cases, so at least $2$ are needed.

2. 2. Strategy

   Weigh $3$ vs $3$. If they balance, weigh the remaining $2$ against each other. Otherwise, from the heavy group of $3$, weigh $1$ vs $1$.

3. 3. Key idea

   Weighing puzzles are information problems: split into three groups as equal as possible.

Answer: 2