Vedadots
Q3031/80Q32
Q31·CSAT · Prelims 2026

Optimization — Weighing Scale Logic

ReasoningMatrix PuzzleSeries & Pattern● Medium

Question

Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty? [cite: 4060, 4061, 4062]

Options

a

2

Answer
b

3

c

4

d

1

Explanation

To optimize the identification of a lighter item using a simple two-pan balancing scale, split the group into three components rather than two (ternary search logic)[cite: 4060, 4061, 4062].

Attempt 1: Group the 7 cubes into segments of 3, 3, and 1. Place 3 cubes on the left pan and 3 cubes on the right pan, leaving 1 cube aside.
Scenario A: If the scale balances evenly, the odd lighter cube must be the 1 left aside. (Identified with certainty in 1 attempt).
Scenario B: If the scale tilts, the pan that goes up contains the lighter cube out of that group of 3. Proceed to the next step with those 3 cubes.
Attempt 2: Take the 3 suspect cubes from the lighter pan and place 1 on the left pan and 1 on the right pan, leaving 1 aside.
Scenario A: If the pans balance evenly, the lighter cube is the 1 left aside.
Scenario B: If the scale tilts, the pan that goes up contains the lighter cube.

Thus, a maximum of 2 attempts guarantees identifying the defective lighter cube with absolute certainty under any scenario.

For beam balance scale problems, dividing the total item pool into a three-part distribution maximizes the information gained per weighing step.

Answer: (a).

Question details

Year

2026

Paper

CSAT

Question

Q31

Section

Logical Reasoning

Sub-topic

Matrix Puzzle

Type

Series & Pattern

Difficulty

Medium

Source hint

Weighing balance — binary and ternary search algorithms

See all questions on Matrix Puzzle

Browse every tagged question across all years

Explore →
Back to CSAT 2026