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Contest you're preparing for
Equations, inequalities, functions, and algebraic structure—the core of most contest problems.
Counting, bijections, pigeonhole, and clever ways to enumerate possibilities without missing cases.
Synthetic and coordinate angles: triangles, circles, areas, and spatial reasoning.
Divisors, primes, modular arithmetic, and Diophantine ideas that show up everywhere.
Discrete probability, expectation, and careful case analysis when outcomes are not equally likely.
Triangles, identities, and trig substitutions that simplify tough algebra and geometry.
AM–GM, Cauchy–Schwarz, smoothing, and bounds that tame messy expressions.
Recursions, closed forms, growth rates, and patterns across indexed families.