Seen It Before

Pólya's question for a stuck solver: have you seen it before, or the same problem in a slightly different form? Answer it for the user. Your deliverable is the mapping, given in the conversation: which Classic problems the user's problem is a Variant of, and what their known solutions offer it. The mapping stops there; direction for carrying out the specific task (libraries, vendor docs, changes to the repo) is $dont-know-how's.

If the user passed an argument, it is the problem. Otherwise take the problem the user is stuck on in the conversation.

A Classic problem is a named, well-studied problem from any field (algorithms, distributed systems, operations research, economics, game theory, statistics, and beyond) whose known solutions a reliable source documents. The user's problem is a Variant when it shares a Classic problem's structure and departs from it in specific, named ways. The user need not know any names; finding them is your job.

1. Strip it to the skeleton

Rewrite the problem as one sentence of pure structure: what is being decided or computed, under which constraints, against which unknowns. Replace every domain noun (the product, the service, the team) with the role it plays.

Done when the skeleton names the decision, the constraints, and the unknowns, and carries none of the user's domain nouns.

2. Find candidates

Search every field for Classic problems with the skeleton's shape. Match on structure, never on shared vocabulary: whether to automate a recurring manual step is a ski rental problem; screening applicants one at a time is optimal stopping.

For each candidate, work out: