The Question
You have 8 identical balls. One is slightly heavier than the rest. Using a balance scale only twice, how do you find the heavier ball?
This is one of the most reported brain teasers from consulting and banking interviews, including McKinsey. It looks simple, but most candidates waste their first weighing. The trick is to divide, not guess.
The Answer
Weigh 3 balls against 3 balls first. Then weigh 1 against 1 from the heavier group.
Two weighings, guaranteed to find the heavier ball every time. Here is exactly how.
Step-by-Step Solution
Weighing 1: 3 vs 3
Place 3 balls on the left pan and 3 balls on the right pan. Leave 2 balls aside. There are three possible outcomes:
- Left side goes down: the heavier ball is among the 3 on the left.
- Right side goes down: the heavier ball is among the 3 on the right.
- Perfectly balanced: the heavier ball is one of the 2 you set aside.
Either way, you have narrowed 8 suspects down to 3 (or 2).
Weighing 2: 1 vs 1
Take the suspect group from weighing 1:
- If you have 3 suspects: put 1 on each pan, leave 1 aside. If a pan goes down, that ball is heavier. If balanced, the ball you set aside is the heavier one.
- If you have 2 suspects: put 1 on each pan. The pan that goes down holds the heavier ball.
Done. The heavier ball is identified in exactly 2 weighings.
Why This Works
Each weighing on a balance scale gives you three outcomes (left heavy, right heavy, balanced), not two. That means 2 weighings can distinguish between 3 x 3 = 9 possibilities, which is more than enough for 8 balls.
The common mistake is weighing 4 against 4 first. That only tells you which half contains the heavier ball, leaving 4 suspects and just 1 weighing. With 4 suspects and 1 weighing (3 outcomes), you cannot finish. The 3-3-2 split is the only first move that works.
What the Interviewer Is Testing
- Information theory thinking: Do you see that a balance scale gives 3 outcomes per weighing, and plan around that?
- Systematic elimination: Can you design a strategy that works in every case, not just the lucky one?
- Avoiding the obvious trap: The 4-vs-4 first weighing feels natural but fails. Interviewers watch for who catches this.
If you get stuck, say your thinking out loud. “Each weighing has three outcomes, so I need to split the balls to use all three” shows the interviewer you understand the structure even before you land the answer.
More Interview Brain Teasers
- Goldman Sachs: 4 cars, 1000 miles of fuel each, what is the maximum distance?
- Why are manhole covers round? (Coming soon)
- How many golf balls fit in a school bus? (Coming soon)
Lauren Brooks is a finance professional writing on professional exams, study strategies, and finance careers.
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