VLSI DV Interview Puzzles · All levels

9 Balls, 1 Heavier, 2 Weighings

Nine identical-looking balls contain exactly one heavier ball. Using a balance scale and at most two weighings, identify the heavy ball.

Puzzle

Difficulty: Easy · Puzzle 1 of 6 · Topic: Classic Brain Teasers

Nine identical-looking balls contain exactly one heavier ball. Using a balance scale and at most two weighings, identify the heavy ball.

Hint

First weighing should split candidates into three equal groups.

Step-by-step solution

diagram

1) Split into groups A, B, C with 3 balls each. Weigh A vs B.
2) If A or B is heavier, heavy ball is inside that heavier trio. If equal, heavy ball is in C.
3) Take the identified trio and weigh one ball vs one ball.
4) If one side is heavier, that ball is the answer; if equal, the unweighed ball is heavier.
5) Why two weighings are enough: each weighing has 3 outcomes (left heavy, right heavy, equal), so 3^2 = 9 distinguishable cases.

Answer

Answer: Use a 3-3-3 split, then a 1-vs-1 inside the identified trio; two weighings always isolate the heavy ball.

Why candidates get it wrong

Treating it like binary search; a balance gives ternary information, not binary.

Interviewer follow-up

If one ball could be either heavier or lighter among 12 balls, how many weighings are needed?

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