Twelve Coins Lower Bound

Count the possible scenarios.

Each weighing has three outcomes.

1. 1. Scenarios

   $12$ coins $\times$ $2$ (heavy or light) $=24$ cases.

2. 2. Bound

   Two weighings give at most $3^2=9$ outcomes $<24$, so at least $3$ are needed (and $3$ suffice).

3. 3. Key idea

   Compare the number of cases to $3^k$ to bound any weighing puzzle.

Answer: 3