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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.

4 votes

Lotteries, Turan's problem, and minimization of risk

This is not a real "answer" but an observation. Each 6-tuple has ${6 \choose 4}$ 4-tuples, so it stands to reason that once $N$ is some smallish multiple $m$ of ${50\choose 4}/{6\choose 4}$ then Bob's …
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