Twenty-Seven Coins, One Heavy

Each weighing can rule out two thirds of the coins.

$3^3=27$.

1. 1. Bound

   Two weighings separate only $9$ cases.

2. 2. Strategy

   Groups of $9$, then $3$, then $1$: three weighings.

3. 3. Key idea

   Ternary search is optimal whenever the counterfeit's direction is known.

Answer: 3