Max Infection Spread at Dinner

This brain teaser is about how a contagion spreads through a fully mixed group when every interaction must be unique. It lives at the intersection of combinatorics, graph theory, and stochastic thinking, even though the answer is ultimately deterministic. On MyQuantPartner, problems like this sit in the "hard" bucket of quant prep because they force you to reason about structure rather than just compute.

It trains your ability to see hidden constraints in a random-looking process, formalize them as a network, and reason about worst-case dynamics. You practice identifying bottlenecks, understanding how local rules aggregate into global behavior, and manipulating interaction patterns abstractly.

This matters in quant interviews because real trading systems behave like networks under constraints. Interviewers want to see you reason about propagation, adversarial scenarios, and limits, which underlies market impact, order routing, and risk transmission.

What it tests

The core structure governing this class of problems is the interplay between combinatorial pairing constraints and the propagation of a property (like infection) through a network. When each individual must interact with every other exactly once, the process is governed by the maximal time it takes for information (or infection) to traverse the most resistant path in the network, under the worst-case arrangement. The principle is that the slowest possible spread occurs when the network is partitioned into subgroups that minimize cross-group interactions, so the property can only jump from one group to the next after all intra-group interactions are exhausted. The maximal time is then determined by the number of groups, the size of each group, and the requirement that each pair must be unique, which together define the bottleneck for full propagation. This pattern holds because the structure of the interaction schedule, not the randomness of infection, dictates the upper bound on spread.