A hundred cars, random speeds, no overtaking: how many clusters form on average?

A hundred cars with different top speeds in random order on an endless road with no passing. Fast cars get stuck behind slow ones. The story asks the expected number of clusters. You type your answer and check it. Then you step through the answer and the breakdown.

Why quant interviews test this

Spot the record-low pattern and write the count as a sum of indicators. The written solution is at /brain-teasers/single-lane-cars/solution.

The Cars on a Single-Lane Road guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

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