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Book Exercise Lanes

This module's exercise system is partly book-driven (Dromey chunks) and partly self-curated (problems from previous modules plus external sources listed in resources.md). Use these lanes for targeted volume after you have already learned the concept from the guide.

How To Use This Page​

  1. Finish the relevant concept page first.
  2. Solve at least one problem of your own from memory.
  3. Only then open the matching exercise lane.
  4. Keep a mistake log with tags such as bad problem statement, no plan, skipped verification, pattern after 2 examples, invariant not preserved, termination unstated, execution bug misdiagnosed as plan bug.

Lane 1: Polya Discipline​

Use this lane when you solve problems but your four-phase execution is not yet automatic.

Target outcomes:

  • 5 full Polya blocks written on previously solved problems
  • 3 problems where you caught a plan-vs-execution distinction retroactively
  • 2 transfer notes per problem

Lane 2: Heuristic Selection and Working Backwards​

Use this lane when you default to forward search on everything and want to build the reflex to reach for alternatives.

Supplementary exercise pool (from Modules 1-4):

  • 10 proof problems from Module 1 that can be reworked with special-cases or working-backwards
  • 8 counting problems from Module 2 that reveal a pattern on small cases
  • 6 probability problems from Module 3 that benefit from backward conditioning

Target outcomes:

  • 6 problems attacked by working backwards with explicit backward-implication chain
  • 6 problems attacked by special-cases with n=2, 3, 4 worked before the general argument
  • 4 analogy notes ("this is just like ...") with structural justification

Lane 3: Invariants, Construction, and Paradigm Choice​

Use this lane when you can prove things but have not built the reflex to choose among invariant, contradiction, construction, D&C, and DP.

Target outcomes:

  • 4 invariant or monovariant arguments with the invariant stated explicitly
  • 4 contradiction arguments with all three skeleton parts labeled
  • 4 constructive proofs with termination, correctness, and effectiveness arguments
  • 3 divide-and-conquer problems with explicit recurrence
  • 3 DP problems with explicit recurrence and memoization strategy

Lane 4: Debugging Reasoning and Growth​

Use this lane when your final answers improve but your self-diagnostic skill does not.

Target outcomes:

  • 8 reasoning bugs classified into model / plan / execution categories
  • 5 minimal counterexamples built for bugs that initially seemed complex
  • 3 rubber-duck logs where the act of explaining surfaced the bug
  • 1 self-bug-profile memo naming the two or three error categories most common for you

Lane 5: Bridge to Computing​

Use this lane when you can solve textbook problems but stall on informal product prompts, unfamiliar code, or work that must finish in a fixed window.

Target outcomes:

  • 3 informal prompts translated into full formal specs (inputs, outputs, invariants, tie-breaking, failure modes, determinism, one performance constraint)
  • 3 unfamiliar 30-60 line functions read without running, with invariant and termination measure written, then compared to the actual behavior on n = 0, 1, 2
  • 2 triage drills: a timed scenario (30-60 min cap) where you list sub-problems, rank them by information-per-minute, and deliver a defensible writeup at the deadline

Self-Curated Problem Set​

Build a custom set with these minimums, drawn from Modules 1-4, external sources in resources.md, or your own work:

  • 5 Polya-full problems with all four phases in writing
  • 5 heuristic-classified problems with the chosen heuristic defended in one sentence
  • 5 invariant or contradiction arguments
  • 5 constructive proofs doubling as algorithms
  • 5 divide-and-conquer or DP problems with recurrences

Completion Checklist​

  • Completed at least two lanes in full
  • Logged at least 12 real reasoning bugs and the category of each
  • Wrote at least 15 full Polya blocks in writing
  • Reattempted at least 4 failed problems after re-planning (not just re-executing)
  • Added at least 10 transfer notes to a permanent problem journal