You have 8 identical-looking balls; one is heavier. Using a balance scale, what is the minimum number of weighings to find it?
Interviewer Expectations for this Question
01
Core Competency
Assesses fundamental understanding of Aptitude & Reasoning conventions, runtime behavior, and memory/performance considerations.
02
Evaluation Criteria
Hiring managers look for precision, avoidance of ambiguous jargon, and ability to explain trade-offs under real production conditions.
Comprehensive Model Answer
Verified Solution
Two weighings.
Weighing 1: split into 3, 3 and 2. Weigh the two groups of 3.
- If one side is heavier, the heavy ball is in that group of 3.
- If they balance, the heavy ball is in the group of 2.
Weighing 2:
- If in a group of 3: weigh one against another. If one is heavier it is the ball; if they balance, the third one is heavy.
- If in a group of 2: weigh them against each other; the heavier is the answer.
General principle: with a balance scale each weighing has three outcomes, so b weighings distinguish up to 3^b cases. For 8 balls, 3^2 = 9 >= 8, so two weighings suffice.
Candidate Response Strategy & Interview Tips
- Start with a concise one-sentence summary: Deliver a direct, confident answer first before expanding into nuances.
- Demonstrate real-world trade-offs: Discuss where this approach excels and when you would avoid it in production systems.
- Discuss complexity & edge cases: Proactively explain time/space complexity or boundary conditions (null values, scale limits).
- Prepare for interviewer follow-ups: Technical hiring panels frequently probe deeper into concurrency, backward compatibility, or alternative libraries.