Overview
Scaling the counterfeit-coin hunt from eight coins to twelve shows the real power of a three-outcome balance: information, not effort, is the limiting resource.
How to solve The Twelve Coins
- Split the twelve coins into three groups of four and weigh two of them.
- Balance or tilt narrows the heavy coin to a single group of four.
- Repeat within that group; three weighings always suffice.
The key insight
Each weighing has three outcomes, so k weighings distinguish 3^k cases. Three weighings cover up to 27 coins — twelve is comfortably within reach.
Variations & echoes
- The hardest classic has 12 coins where you don't know if the fake is heavier or lighter — still three weighings.
- It's a concrete instance of information theory's counting bound.
Frequently asked questions
How many coins can 3 weighings handle?
Up to 27 when you know the fake is heavier (3³). The unknown-direction version handles fewer.