Category
Algebra
Polynomials, inequalities, and the art of a clean substitution.
Algebra is where most competition problems begin. Polynomials, inequalities, sequences, functional equations — the objects are familiar from school, but a contest asks you to manipulate them rather than merely evaluate them.
The problems here run from a single-step factorisation up to identities that only fall to a well-chosen substitution. Expect Vieta’s formulas, AM–GM, and the recurring lesson that the right rearrangement does most of the work.
Latest problems
243 problems
Sum of Real Roots
1000
2
Sum of Squares of Cubic Roots
1000
3
Summing a Floor Function
1000
2
Terms Shared by Two Sequences
1000
2
The Real Part of a Power
1000
2
Train Speed Problem
1000
2
When a Quadratic Has Real Roots
1000
1
Work Problem with Two People
1000
1
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