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 When Bool Isn't Enough: Enriching a Tree Fold — Fold with an enriched result type
27. 027 A Seed With Two Jobs: Digits Most-Significant-First — Unfold with a control-carrying seed
28. 028 Tree Unfold: Building a Balanced BST From a Range — Tree unfold
29. 029 Fold ∘ Unfold: Never Build the Tree At All — Fold ∘ Unfold (fusion)
30. 030 Eager vs Lazy: Counting the Wasted Work — Eager vs lazy evaluation
31. 031 Infinite Structures via Laziness: A Stream of Naturals — Infinite structures via laziness
32. 032 Runaway Recursion: When an Eager Definition Can Never Bottom Out — Runaway recursion
33. 033 Tail Calls: What an Accumulator Actually Buys You — Tail calls & accumulators

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 The Ordering Doesn't Vanish, It Cancels — Binomial likelihood as a ratio between hypotheses
17. 017 Four Times the Trials, Half the Spread — Posterior SD scales as 1/sqrt(n), not 1/n
18. 018 Don't Just Square the Mean — Posterior predictive: what do you expect next?
19. 019 Same Data, Either Order — Yesterday's posterior is today's prior (order of evidence)
20. 020 One Update, Two Distributions — Conjugacy: beta-binomial and normal-normal
21. 021 Five Settings, No Formula — When conjugacy breaks: grid approximation preview
22. 022 Which Single Number Do You Report? — Point estimates are loss-function choices
23. 023 What the 90% Actually Covers — Credible intervals vs confidence intervals

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 The Winner With Nothing Left to Win — Blackboard control: agenda scoring needs a value term
15. 015 Three Stale Uses Beat One Fresh One — ACT-R base-level activation: summing decay across every past use
16. 016 Why This Puzzle System Quizzes You Instead of Just Explaining — Encoding vs retrieval; recognition vs recall; retrieval practice
17. 017 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)
18. 018 Change One Requirement, Flip the Architecture — Blackboard vs. pipeline: mutual revision, not predefined order
19. 019 Good Enough, On Purpose — Satisficing (Simon): why real agents don't optimize
20. 020 The Probable Story That Can't Be More Probable — Heuristics & biases: representativeness and the conjunction fallacy
21. 021 Two Systems, or One System With a Threshold? — Dual-process accounts: what System 1/2 explains, and what it hand-waves

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
17. 017 Same Detector, Rarer Fraud: Precision Collapses — Class imbalance: precision depends on prevalence, recall doesn't
18. 018 Audit This Churn Pipeline Before It Ships — Leakage in practice: naming the type, writing the fix, and the prediction-time test
19. 019 Building the Calibration Curve From Scratch — Calibration: building the curve by hand from raw (score, label) pairs
20. 020 Attention's Real Advantage Isn't Accuracy — It's Span — Why transformers parallelize: work vs. span, and vanishing gradients revisited as the cost this avoids
21. 021 More Data, More Params, More Compute: Which Buys What? — Scaling intuitions: what more data, parameters, and compute each buy — and where each runs out
22. 022 When the Simple Model Wins — Bias/variance in the wild: when a linear model beats a deep one
23. 023 The Metric Went Up. The Goal Didn't. — Goodhart's law: optimizing the metric vs. the goal
24. 024 The Ticket: Something's Wrong With Production — Capstone: diagnosing a broken pipeline from evidence, using every failure mode this run covered