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Socrates — hello world
Animals Friends Paths
Family cousins — generations and branches
Good cobbler — structured descriptions
Schema inference — classes and properties
French cities
Shortest path — minimum route costs
Dijkstra — a sorted shortest-path frontier
GPS — choosing a route
Path discovery — bounded routes across the full airport graph
Lists — concatenation, squares, and sums
Unification — list splits and repeated variables
Text processing — Unicode codes and exact decimal parsing
Term structure — generic record validation and construction
Hanoi — moving three disks
Peano arithmetic — symbolic natural numbers
Collatz — trajectories from 1 through 20
Sieve — primes through 100
Peasant arithmetic — halving and exact integers
Arithmetic — exact integers and real functions
Age — checking a birthday
Easter — Gregorian dates from 2021 through 2050
Bayes diagnosis — weighing evidence
Ackermann — fast-growing numbers
Fibonacci 10000 Complex numbers Turing machine
Padovan — exact recurrence and plastic ratio
Newton–Raphson — numerical roots
Pell equation — exact Diophantine solutions
Binomial coefficients — exact Vandermonde sums
Group theory — cosets and Lagrange's identity in S3
N queens — 92 eight-queen solutions
Flute puzzle — occupations and instruments
Knapsack — the highest-value feasible pack
Interval scheduling — the highest-value compatible jobs
Job shop — minimum completion time on shared machines
Matrices — exact products and noncommutativity
Modular powers — exact repeated squaring
Polynomial roots — complex coefficients through degree four
Least squares — slope, intercept, and R²
FFT — eight-point frequency spectra
Hamming code — single-bit error correction
RC filter — time constant and cutoff
Buck converter — current and voltage ripple
Radioactive decay — activity and half-lives
Cantilever beam — elastic tip deflection
Orbital transfer — Hohmann delta-v and time
Braking — reaction distance and friction
Nitrogen budget — losses, deficits, and surpluses
Expression evaluation — a graph of operations
State transitions — an account event log
Control system — actuator commands
Interval relations — all thirteen cases
Gray-code counter — logic gates and clock pulses
Wind turbine — maintenance conditions
Inventory — line totals and an invoice
Statistics — population mean, variance, and deviation
Vectors — dot products, norms, and cosine similarity
Type inference — annotated expressions and lexical scope
Symbolic differentiation — explicit expression trees
Critical path — project timing and delaying dependencies
EV depot — charger choices, blockers, and required changes
Outage recovery — redundant services and least-cost repairs
Static analysis — signs, loops, and division warnings
Battery dispatch — charging plans, reserves, and energy costs
Research portal — comparing rulebooks
Dog license — counting owned dogs
Permissions — roles and suspension exclusions
Access control — all, any, and none conditions
Policy risk — ranked findings and mitigations
Log correlation — parse events and explain trace alerts
Data quality — values, references, required fields, and keys
Software supply chain — exposures, waivers, and upgrade plans
Animal observations — conflicting evidence
Delfour Negation Aggregation
List collection — pick lists from order lines
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