Hard · Probability & Combinatorics · Numerical · ~12 min · #68

Break the Longer Piece

Real interview · Goldman Sachs

Break a stick of length 1 at a uniformly random point. Then take the longer of the two pieces and break it at a uniformly random point along its length.

What is the probability that the three pieces can form a triangle?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

Reported in interviews

Goldman SachsGlassdoor interview question

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Triangle inequalityConditioning on the first break

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