Medium · Brain Teasers & Logic · Numerical · ~7 min · #93

A Hundred Ants on a Stick

Real interview · J.P. Morgan

100 ants start at independent uniform positions on the interval $[0, 1]$ . Each walks at speed 1 toward a randomly chosen end. When two ants meet, both reverse direction. An ant leaves when it reaches an end.

What is the expected time until the last ant has left?

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Worked solution

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

Reported in interviews

J.P. MorganGlassdoor interview question
Reported as how long the last ant takes. We specify independent positions and ask for the mean.

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

Relabelling symmetryOrder statistics

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