Learn: Daily Thinking Puzzles

All lessons

Functional & parallel thinking

1. 001 Spot the Pure Function — Pure functions
2. 002 The List That Wouldn't Change — Immutability
3. 003 Sum a List Without a Loop — Recursion over lists
4. 004 Find the Last Element — Recursion: base-case design
5. 005 Count the List — Recursion: counting & accumulators
6. 006 Reverse a List — Twice — Recursion: efficiency & accumulators
7. 007 The Substitution Game — Referential transparency
8. 008 Push the Effects to the Edge — Side effects at the boundary
9. 009 Find It, Then Transform It — Recursion: membership & transform
10. 010 Keep, Drop, and Slice — Recursion: filter, take, drop
11. 011 Flatten the Nesting — Recursion: nested structures
12. 012 Tail Calls and the Accumulator Pattern — Tail recursion
13. 013 Functions Are Values — Functions as values
14. 014 Build Map and Filter — Building map and filter
15. 015 Build the Fold — Fold / reduce
16. 016 Closures Capture Variables, Not Values — Closures
17. 017 Curry, Partial, Compose — Currying & composition
18. 018 Reduce Reconstructs Everything — Reduce as universal
19. 019 Sum Types and Product Types — Algebraic data types
20. 020 Pattern Matching: Exhaustive Case Analysis — Pattern matching
21. 021 A Tree in a Box: Binary Trees and Recursion — Binary trees
22. 022 Mirroring and Summing a Binary Tree — Tree recursion
23. 023 Fold as Elimination: The Tree Fold — Fold over ADT
24. 024 Represent, Then Erase: Expression Trees — Data as programs
25. 025 Unfold: Generating Structures from Seeds — Unfold
26. 026 Tree Unfold: Building Trees Top-Down — Tree unfold
27. 027 Fold ∘ Unfold: Build Then Consume — Fold ∘ Unfold
28. 028 Eager vs Lazy Evaluation — Eager vs lazy evaluation
29. 029 Infinite Streams via Laziness — Infinite streams
30. 030 Runaway Recursion: When Eager Definitions Explode — Runaway recursion
31. 031 Tail Calls: The Recursion That Doesn't Grow the Stack — Tail calls & tail-call optimization
32. 032 Sharing vs Recomputation: The Hidden Cost of Naive Fibonacci — Sharing vs recomputation
33. 033 What Happens Next: Continuation-Passing Style — Continuation-passing style (CPS)

Bayesian statistics

1. 001 Two Meanings of 70% — Probability as plausibility
2. 002 One Table, Three Questions — Joint, marginal, conditional
3. 003 Chaining Plausibilities — Multiplication rule
4. 004 When Multiplying Is Legal — Independence
5. 005 The Information in the Telling — Conditioning on how you learned it
6. 006 Bayes from Both Directions — Bayes' theorem
7. 007 The Test Is 99% Accurate. You're Probably Fine. — Base rates
8. 008 The Transposed Conditional — Prosecutor's fallacy
9. 009 Odds Do the Arithmetic For You — Odds form of Bayes' theorem
10. 010 Two Tests, One Multiplication (Usually) — Sequential evidence & conditional independence
11. 011 The Bet a 90% Interval Makes — Calibration seed: estimation & 90% intervals
12. 012 The Answer Sheet That Must Sum to One — Distributions as answer sheets (pmf)
13. 013 What 4 Heads Out of 5 Actually Says — The binomial likelihood
14. 014 Choosing a Starting Answer Sheet — Priors: uniform, informative, and letting the data speak
15. 015 The Update That's Just Addition — Beta-binomial updating: posterior = prior counts + observed counts
16. 016 How Much Does One More Observation Move You? — Watching the posterior sharpen; how much one observation moves you

Cognitive science & AI architectures

1. 001 Three Questions About One Mind — Marr's levels
2. 002 Seven, Plus or Minus Two — Working memory & chunking
3. 003 The Recognize–Act Cycle — Production systems
4. 004 Experts Around a Blackboard — Blackboard architecture
5. 005 Growing Outward From an Island — Hearsay-II anatomy
6. 006 Scoring the Agenda — Blackboard control & the agenda
7. 007 Two Systems, One Architecture Question — Blackboard vs. pipeline/message-passing
8. 008 The Blackboard, Fifty Years Later — Blackboards in modern agent harnesses
9. 009 Knowing That vs. Knowing How — ACT-R: declarative vs. procedural memory
10. 010 The Number Behind Forgetting — ACT-R: spreading activation & base-level decay
11. 011 The Architecture That Refuses to Get Stuck — SOAR I: problem spaces, universal subgoaling, impasses
12. 012 Never Solve the Same Impasse Twice — SOAR II: chunking as learning
13. 013 Where the Architectures Actually Get Checked — What these architectures predict about humans, and how well
14. 014 Why This Puzzle System Quizzes You Instead of Just Explaining — Encoding vs retrieval; recognition vs recall; retrieval practice
15. 015 Why 'Doctor' Makes You Faster to Recognize 'Nurse' — Spreading activation & priming
16. 016 What Gets Through the Filter — and What Doesn't — Attention as selection: dichotic listening, inattentional blindness, the binding problem
17. 017 The Amnesiac Who Learned to Juggle and Never Knew It — Long-term memory systems: episodic vs semantic vs procedural
18. 018 Why Your 100th Repetition Barely Feels Faster Than Your 90th — The power law of practice; what gets faster and what doesn't
19. 019 The Chess Master's Memory Isn't What You Think It Is — Expertise as chunking + retrieval (de Groot's chess studies, Chase & Simon)
20. 020 Ten Years of Experience, or One Year Repeated Ten Times? — Deliberate practice and its limits; transfer (and its scarcity)
21. 021 Why This Path Won't Let You Do 20 Lessons on One Topic in a Row — Spacing & interleaving (the science this whole puzzle system is built on)

Machine learning

1. 001 Guess the Function — Learning as function fitting
2. 002 The Exam You've Already Seen — Train/test split
3. 003 The Too-Flexible Curve — Overfitting
4. 004 The Dumbest Model in the Room — Baselines
5. 005 The Bedroom That Costs You Money — Linear regression & coefficient interpretation
6. 006 Rolling Downhill, Too Fast — Loss surfaces & gradient descent
7. 007 Squashing a Line Into a Probability — Logistic regression
8. 008 The Penalty That Shrinks the Fit — Regularization
9. 009 The Tree That Memorized the Forest — Decision trees
10. 010 Averaging Away the Wobble — Bagging & random forests
11. 011 Chasing the Leftover Error — Boosting: stacking weak learners on residuals
12. 012 The Importance Score That Lied by Omission — Feature importance skepticism
13. 013 One Split Isn't Enough to Trust — Cross-validation: what it estimates, and how to leak through it
14. 014 The Feature That Knew the Answer Already — Leakage: target, temporal, and group leakage
15. 015 Two Systems, Same Accuracy, One Useless — Class imbalance: accuracy lies; precision/recall
16. 016 When '90% Confident' Means 70% Right — Calibration: when a stated probability matches the observed rate