Solve two logic brain teasers

Q: Solve two logic brain teasers

This is a Cognitive Ability / Logic interview question from Citi for Software Engineer roles. View the full question and solution on PracHub.

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Question

Two Classic Logic/Optimization Puzzles

Puzzle 1: Heavier Ball with a Balance Scale

You have 12 visually identical balls. Exactly one ball is heavier than the others; all remaining balls have equal weight. You have a balance scale and may use it at most three times. Determine which ball is heavier and justify that three weighings are both sufficient and necessary.

Notes:

A balance scale comparison yields three outcomes: left side heavier, right side heavier, or balance.
The odd ball is known to be heavier (not lighter).

Puzzle 2: Bridge and Torch

Four people must cross a bridge at night with one torch. Crossing times are 1, 2, 7, and 10 minutes. At most two can cross at a time, and the torch must be carried whenever anyone crosses. Find:

The minimum total crossing time.
A sequence of crossings that achieves it.
A brief proof of optimality (why no faster schedule exists).

Solve two logic brain teasers

Two Classic Logic/Optimization Puzzles

Puzzle 1: Heavier Ball with a Balance Scale

Puzzle 2: Bridge and Torch

Solution (Locked)

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