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Sig·Software Engineer·Technical Phone Screen·Junior

Junior
Jun 2026

Summary

SIG quant researcher interview with a physics/math puzzle about balanced mobiles. Pretty niche stuff, felt more like a math olympiad problem than a typical finance interview.

Questions Asked (1)

Q1

A mobile is structured as a binary tree where each bar splits weight equally between its two sides. If the total weight is 48 lbs and one side keeps branching while the other terminates as a leaf at each level, what is the weight of the leaf hanging at the bottom after 4 levels of halving?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

So basically 48 divided by 2 to the fourth power, which is 3 lbs.

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AI HintsAI Generated

Suggested Approach

Model the mobile as a binary tree where each split divides the total weight equally between the two branches. Since one side continues branching and the other terminates as a leaf at each level, the leaf at each level receives half of the weight that reaches that level. Calculate the weight at the bottom leaf after 4 levels by repeatedly halving the total weight.

Pro tip: Clarify the assumption that the mobile is perfectly balanced and that the branching side carries the remaining weight. This shows attention to detail and prevents misinterpretation.

1. Understand the structure

Visualize the mobile as a binary tree where each bar splits the weight equally between its two sides. One side continues branching, while the other side ends in a leaf at each level.

2. Determine weight distribution

At each level, the total weight is halved between the two sides. The leaf on the terminating side receives half of the weight at that level, and the remaining half goes to the branching side.

3. Calculate leaf weights

Compute the weight of the leaf at each level: Level 1 leaf gets 24 lbs, Level 2 leaf gets 12 lbs, Level 3 leaf gets 6 lbs, Level 4 leaf gets 3 lbs.

4. Identify the bottom leaf

After 4 levels of halving, the leaf at the bottom (Level 4) weighs 3 lbs.

Key Points to Mention

  • Binary tree representation of the mobile
  • Equal weight distribution at each split
  • Halving process at each level
  • Calculation of leaf weights at each level
  • Final weight after 4 levels
  • Assumption of perfect balance and no other forces

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.