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Solve two logic brain teasers

CitiSoftware Engineer · Onsite
MediumSoftware EngineerOnsiteStatistics & Math

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This pair of puzzles evaluates logical deduction and optimization competencies—one testing information-theoretic reasoning with constrained ternary comparisons and the other testing sequencing and scheduling trade-offs for minimal total time—and belongs to the Cognitive Ability / Logic category.

Answer both puzzles: (

  1. You have 12 visually identical balls; exactly one is heavier than the others. Using a balance scale only three times, determine which ball is heavier and justify that three weighings are sufficient and necessary. (
  2. Four people must cross a bridge at night with one torch. Their crossing times are 1, 2, 7, and 10 minutes. At most two can cross at a time, and anyone crossing must carry the torch. What is the minimum total time and what sequence achieves it? Prove optimality.