Courses
The chapters of the club’s booklet “Problem-solving techniques”: each chapter presents a classic technique, with examples, summaries and graded exercises. Exact PDFs from the booklet.
📘 Download the full booklet (PDF)Chapter 0 — Examples and Counterexamples
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 3 page(s)
Why a few examples never make a proof: conjectures, counterexamples and the need for rigorous proof, through 12 exercises (factorials, prime-generating polynomials, the Collatz conjecture…).
▶ Interactive simulation
Chapter 1 — Induction
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 4 page(s)
Proof by induction: Fibonacci numbers, binomial coefficients, exercises and problems (Fibonacci identities, divisibility, tromino tilings…).
▶ Interactive simulation
Chapter 2 — Extremal Principle
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 2 page(s)
Looking at the smallest or largest element: fundamental principles, exercises (irrationality of the square root of 2, points in the plane…) and problems.
▶ Interactive simulation
Chapter 3 — Pigeonhole Principle
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 4 page(s)
If n+1 objects are placed in n boxes, one box holds more than one object: 18 exercises and 12 problems, from birthdays to lattice points.
▶ Interactive simulation
Chapter 4 — Geometry
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 3 page(s)
Vectors, midpoints, centroids and parallelograms: useful notions, 8 exercises and 9 problems in vector geometry and circle geometry.
▶ Interactive simulation
Chapter 5 — Number Theory
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 3 page(s)
Euclidean division, GCD and LCM, congruences, Fermat's little theorem, integer part: definitions, key facts, exercises and problems.
▶ Interactive simulation
Chapter 6 — Combinatorics
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 21 page(s)
Counting without enumerating: additive and multiplicative principles, choice trees, factorials and binomial coefficients, inclusion-exclusion and bijections, with many Malagasy-flavoured examples.
▶ Interactive simulation
Chapter 7 — Invariants
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · 15 page(s)
Finding what never changes: invariants (parity, congruences, colourings, weighted sums, GCD) and monovariants, with 15 graded exercises and 5 complex problems including the fifteen puzzle.
▶ Interactive simulation
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