Which Coin is Fake?

What this coin-weighing logic puzzle tests

This is a medium-difficulty puzzle commonly posed in trading and quant interviews to assess systematic problem-solving under constraints. It requires you to design a decision tree that minimizes worst-case outcomes—a skill directly relevant to risk management and algorithm design in quantitative finance.

The core challenge is to use information theory and logical deduction to narrow down possibilities efficiently. Each weighing has three possible outcomes (left heavier, right heavier, or balanced), and you must account for both the identity of the counterfeit coin and its weight relative to genuine coins. Strong solutions work backwards from the constraints, building a strategy that guarantees resolution within a fixed number of steps regardless of which coin is fake.

• Information-theoretic lower bounds and decision trees
• Systematic case analysis and symmetry
• Worst-case vs. average-case reasoning