The Full Pipeline, No Labels

This module's problems announce nothing. The pipeline runs in order, and each stage has a time box:

1. Model (3–5 min). Objects, quantities, objective, constraints — on paper. No algorithm thought yet.
2. Budget (2 min). Multiply the op count of the obvious approach. The constraint table names the allowed complexity family.
3. Observe (10 min). Compute small cases; run the Big Four scan (invariant, parity, monotonicity, symmetry).
4. Prove (5 min). One exchange argument, one induction, or an honest "unproven hypothesis" tag — which drops the plan's rank.
5. Implement (rest). With the complexity family chosen and the key observation proven, the code is usually the fast part.
6. Attack (before submitting). The five-shape checklist, run against your own solution.

When the pipeline stalls

Stalls happen at stage 3 most often. The escape is reformulation (Module 3): count the complement, reframe the object, decompose the condition. The second escape is the constraint table: a band you can solve is worth real points right now.

The goal state

You know the pipeline is internalized when you can narrate it while solving, without going back to read it. That narration is what the simulations below train.