101 Numbers, Minimum Gap of 1/1000

This quant interview question is about understanding spacing properties of continuous random variables under uniform sampling. It appears in hard quant prep sets because it combines geometric intuition with probability on the unit interval, and requires seeing beyond naive independence assumptions. It is used to probe whether candidates can reason about configurations of many random points subject to global constraints.

It trains your grasp of joint distributions for many uniform draws, conditional probability in high dimension, and the geometry of ordered samples. You must be comfortable mentally moving between a probabilistic description and a geometric picture of feasible regions in continuous space, and seeing how constraints reshape that space.

It matters for quant interviews because similar reasoning appears in order book modeling, event spacing, risk clustering, and rare-event estimation. Strong performance signals readiness for advanced probability puzzles in real quant roles.

What it tests

This problem class is governed by the principle of spacing constraints in random selections, often called the 'gap method' or 'spacing argument.' When selecting objects (numbers, points, or items) with a minimum required separation, the problem reduces to partitioning the total available space into segments: each selection claims a 'forbidden' region around it, and the sum of these forbidden regions must not exceed the total space. The key is that the available space for the remaining selections shrinks with each choice, and the probability is determined by the fraction of the space that remains after accounting for all required gaps. This structure holds because the constraint is global: the sum of all required gaps plus the sum of the 'free' intervals must fit within the total length, and the order of selection does not matter due to symmetry.