Using a balance scale with no weights and exactly three weighings, you have 12 visually identical coins, one of which is counterfeit and either heavier or lighter (unknown). Provide a weighing strategy that always identifies the counterfeit coin and whether it is heavier or lighter. Present the full decision tree: for each weighing, which coins go on each pan and how the next step depends on outcomes (left heavy, right heavy, or balance). Prove correctness and minimality of three weighings.

This question evaluates understanding of combinatorial reasoning, information theory, and decision-tree construction for identifying a single counterfeit coin and whether it is heavier or lighter using constrained balance-scale observations.

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This is a hard difficulty Statistics & Math question, commonly asked during Technical Screen rounds at Coinbase.

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This question is commonly asked for Data Scientist candidates at Coinbase during technical interviews.

Solve the 12-coin balance puzzle | Coinbase Interview Question

12-Coin Counterfeit Problem (3 Weighings)

Setup

You have 12 visually identical coins.
Exactly one coin is counterfeit; it is either heavier or lighter (unknown which).
You have a balance scale and no additional reference weights.

Task

Design a weighing strategy that uses exactly three weighings and always identifies:

which specific coin is counterfeit, and
whether it is heavier or lighter.

Provide the complete decision tree: for each weighing, specify which coins go on each pan, and for each possible outcome (left pan heavy, right pan heavy, or balance), indicate the next step and final identification where applicable.

Finally, prove the correctness of your strategy and that three weighings are minimal (i.e., two weighings cannot always suffice).

12-Coin Counterfeit Problem (3 Weighings)

Setup

You have 12 visually identical coins.
Exactly one coin is counterfeit; it is either heavier or lighter (unknown which).
You have a balance scale and no additional reference weights.

Task

Design a weighing strategy that uses exactly three weighings and always identifies:

which specific coin is counterfeit, and
whether it is heavier or lighter.

Finally, prove the correctness of your strategy and that three weighings are minimal (i.e., two weighings cannot always suffice).

Solve the 12-coin balance puzzle

Quick Overview

12-Coin Counterfeit Problem (3 Weighings)

Setup

Task

Solution

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Solve the 12-coin balance puzzle

Quick Overview

12-Coin Counterfeit Problem (3 Weighings)

Setup

Task

Solution

Comments (0)