Why Mixing Samples Finds Positives in Fewer Tests: The Mathematics of Group Testing and Combinatorial Search
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13 pages
Combinatorics
Can You Recover the Original Numbers When Only the Sum Is Known? The Mathematics of Möbius Inversion
How Can You Design a Deck Where Every Pair of Cards Shares Exactly One Symbol? The World of Finite Geometry
Why Can 100 Prisoners Survive Just by Changing How They Open Boxes? Permutation Cycles, Harmonic Numbers, and Correlation Coupling
What Geometry Emerges When Addition and Multiplication Are Replaced?：Tropical Geometry and the World of Min-Plus Algebra
The Four Color Theorem and the Computer Mathematics Revolution: A Century-Old Enigma and the Philosophy of Mechanical Proof
Inclusion-Exclusion Principle: A Powerful Technique for Correctly Counting Elements in Overlapping Sets
Permutations, Combinations, and the Binomial Theorem: The Beautiful Regularity of Numbers Seen in Pascal's Triangle
Burnside's Lemma: How to Count Patterns When Rotations Matter?
Catalan Numbers: Why Parentheses and Tree Structures Yield the Same Counts
Generating Functions: What's the Benefit of Turning a Sequence into a Function?
Sperner's Lemma: From Coloring Triangles to Existence Proofs
Ramsey Theory: Order Inevitably Emerges from Disorder — Proving Six-Person Relationships with Two Colors
