The Counterfeit Code

🪙 This time, I created a mathematical detective game.

✨ Play The Counterfeit Code

Twelve identical-looking coins lie on your desk. One is counterfeit. It might be heavier or lighter than the others.

You have an old-fashioned balance scale and exactly three weighings to identify the counterfeit coin and determine whether it's heavier or lighter.

I built a playable game with an animated balance, an investigation notebook, and a system that tracks which possibilities remain consistent with your evidence.

There's also a hidden mathematical surprise: you can solve the puzzle using three weighings planned entirely in advance, without adapting your strategy to the results.

The explanation involves a beautiful connection to error-correcting codes and information theory.

I particularly like the underlying arithmetic:

$$\underbrace{12\times2}_{\text{24 possible counterfeit states}} \quad<\quad \underbrace{3^3}_{\text{27 possible sequences of outcomes}}.$$

But can you design three measurements that actually distinguish all 24 possibilities?

The game includes an explicit construction and proof. I tested the interactive solution in a browser.

The whole thing works offline, including on your phone. 🔎