Categories

Descriptions (60 problems)
- Dissections (2 problems)
- Invariants (4 problems)
- Pell's Equation (3 problems)
- Polynomials (13 problems)
  - Games (1 problems)
Graph theory (1 problems)
Problems (1930 problems)
- Algebra (338 problems)
  - Absolute value (5 problems)
    - Absolute value of a number (other) (1 problems)
    - Equations containing absoute values (1 problems)
    - Inequalities containing absolute values (2 problems)
    - Proof by exhaustion (1 problems)
      - Inequalities (1 problems)
  - Algebraic equations and systems of equations (63 problems)
    - Algebraic equations and systems of equations (other) (3 problems)
    - Binomial theorem (2 problems)
    - Diophantine equations (11 problems)
    - Higher order equations. Palindromic polynomial equations (37 problems)
      - Equations of higher order (other) (37 problems)
    - Systems of algebraic non-linear equations (1 problems)
    - Systems of linear equations (2 problems)
  - Algebraic inequalities and systems of inequalities (23 problems)
    - Algebraic inequalities (other) (5 problems)
    - Classical inequalities (3 problems)
    - Linear inequalites and systems of inequalities (6 problems)
    - Number inequalities. Number comparison (3 problems)
    - Quadratic inequalites (several variables) (6 problems)
  - Complex numbers (4 problems)
    - Cartesian form of a complex number, complex conjugate, Argand diagram, etc (3 problems)
  - Diophantine equations (2 problems)
  - Discrete Mathematics (1 problems)
    - Combinatorics (1 problems)
  - Exponential functions and logarithms (6 problems)
    - Exponential functions and logarithms (other) (4 problems)
    - Exponential inequalities (1 problems)
  - Fractions (3 problems)
    - Simple fractions (3 problems)
  - Functional equations (5 problems)
  - Graphs and locus of points on the Cartesian plane (18 problems)
  - Inequalities (3 problems)
  - Mean values (54 problems)
  - Pascal triangle (14 problems)
  - Polynomials (28 problems)
    - Algebraic identities for polynomials (9 problems)
      - Factoring polynomials (6 problems)
      - Identical transformations (3 problems)
    - Cubic polynomials (1 problems)
    - Division of polynomials with remainders. The greatest common divisor (GCD) and the least common multiple (LCM) for polynomilas. (3 problems)
    - Polynomial remainder theorem (little Bezout's theorem). Factorisation. (2 problems)
    - Polynomials(other) (3 problems)
    - Polynomials with integer coefficients and integer values (3 problems)
    - Quadratic polynomials (8 problems)
      - Investigating the quadratic polynomial (4 problems)
      - Quadratic equations and systems of equations (2 problems)
      - Quadratic equations. Formula for the roots. (1 problems)
      - Quadratic equations. Vieta's rule. (2 problems)
    - Symmetrical polynomials (1 problems)
    - Vieta's Formulas (1 problems)
  - Rational functions (5 problems)
    - Identical transformations (2 problems)
    - Inequalities. Method of Intervals. (1 problems)
    - Rational equations (2 problems)
  - Sequences (62 problems)
    - Fibonacci (11 problems)
    - Progressions (12 problems)
      - Arithmetic progression (7 problems)
      - Geometric progression (5 problems)
    - Recurrence relations (1 problems)
      - Fibonacci numbers (1 problems)
    - Recurrent relations (30 problems)
      - Fibonacci numbers (10 problems)
      - Linear recurrent relations (6 problems)
      - Recurrent relations (other) (14 problems)
    - Sums of number sequences and difference series (2 problems)
  - Surds. Rational powers (12 problems)
    - Irrational equations. (7 problems)
    - Irrational inequalities. (3 problems)
    - Square roots (1 problems)
  - Trigonometry (15 problems)
    - Inverse trigonometric functions (2 problems)
    - Systems of trigonometric equations and inequalities (1 problems)
    - Trigonometrical equations (4 problems)
    - Trigonometrical inequalities (2 problems)
    - Trigonometry (other) (5 problems)
- Algebra and arithmetic (24 problems)
  - Algebraic geometry (4 problems)
    - Cryptography (4 problems)
  - Arithmetics. Mental maths (18 problems)
  - Number systems (1 problems)
    - Binary number system (1 problems)
- Algebra and arithmetics (2 problems)
  - Number theory. Divisibility (2 problems)
    - Divisibility rules (2 problems)
      - Divisibility tests for 3 and 9 (1 problems)
- Arithmetic puzzles (3 problems)
- Calculus (106 problems)
  - Derivative (13 problems)
    - Convexity and concavity (1 problems)
    - Derivative and multiple roots (4 problems)
    - Increasing and decreasing. Researching functions (8 problems)
  - Functions of one variable. Continuity (16 problems)
    - Certain properties of a function and recurrence relations. (4 problems)
    - Continuous functions (general properties) (1 problems)
    - Functions. Continuity (other) (2 problems)
    - Monotonicity, boundedness (3 problems)
    - Periodicity and aperiodicity (6 problems)
  - Functions of several variables (1 problems)
  - Integral (1 problems)
    - Applications of integration (1 problems)
      - Area by integration (1 problems)
  - Number sequences (16 problems)
    - Boundedness, monotonicity (2 problems)
    - Limit of a sequence, convergence (9 problems)
    - Number e (1 problems)
    - Number sequences (other) (4 problems)
  - Real numbers (59 problems)
    - Countable and uncountable subsets (2 problems)
    - Integer and fractional parts. Archimedean property (39 problems)
    - Rational and irrational numbers (17 problems)
- Combinatorics (5 problems)
- Constructions (1 problems)
  - Geometry (1 problems)
- Cube nets (1 problems)
- Discrete Mathematics (862 problems)
  - Algorithm Theory (220 problems)
    - Balance puzzles (19 problems)
    - Cooperative algorithms (2 problems)
    - Game theory (98 problems)
      - Fun games (6 problems)
      - Game theory (other) (34 problems)
      - Symmetric strategies (22 problems)
      - Winning and loosing positions (39 problems)
    - Game Theory (1 problems)
    - Theory of algorithms (other) (92 problems)
  - Combinatorics (318 problems)
    - Colorings of the board (18 problems)
    - Discrete geometry (other) (2 problems)
    - Dissections, partitions, covers and tilings (63 problems)
      - Covers (17 problems)
      - Dissections with certain properties (8 problems)
      - Features of dissection pieces (3 problems)
      - Paritions of figures in segments (2 problems)
      - Tilings with ordinary and domino tiles (22 problems)
      - Various dissection problems (6 problems)
    - Geometry on grid paper (19 problems)
    - Integer lattices (14 problems)
      - Integer lattices (other) (12 problems)
      - Polygons and polyhedra with vertices in lattice points (2 problems)
    - Number Theory (1 problems)
    - Packing problems (2 problems)
    - Painting problems (33 problems)
    - Permutations (36 problems)
    - Systems of points and line segments (10 problems)
      - Center of mass (1 problems)
        
        Center of mass formula (1 problems)
      - Systems of points (1 problems)
      - Systems of points and line segments (counterexamples) (1 problems)
      - Systems of points and line segments (other) (3 problems)
      - Systems of points, lines, and line segments (3 problems)
  - Game Theory (5 problems)
  - Game theory (1 problems)
  - Graph Theory (3 problems)
  - Mathematical logic (1 problems)
  - Set theory and logic (323 problems)
    - Linguistics (2 problems)
    - Logic and set theory (33 problems)
    - Mathematical logic (258 problems)
      - Mathematical logic (other) (135 problems)
      - Paradoxes (14 problems)
      - Puzzles (56 problems)
      - Weightings (1 problems)
    - Order relations (10 problems)
    - Set theory (17 problems)
      - Inclusion-exclusion principle (6 problems)
      - Set cardinality. One-to-one correspondence (1 problems)
      - Set theory (other) (2 problems)
      - Union, intersection, and set difference (4 problems)
      - Unusual constructions (2 problems)
- Dissections (2 problems)
  - Pythagorean Theorem (1 problems)
- Fun Problems (142 problems)
  - Arithmetic Puzzles (2 problems)
  - Aritmetic Puzzles (1 problems)
  - Covers (1 problems)
  - Dissections (3 problems)
  - Joke Problems (25 problems)
  - Linguistics (1 problems)
  - Tilings (1 problems)
  - Word Problems (106 problems)
    - Combined labour (work) problems (1 problems)
    - Motion problems (7 problems)
    - Percentages and ratios (8 problems)
    - Solving problems by inequalities. Going through the cases. (5 problems)
    - Tables and tournaments (80 problems)
      - Chessboards and chess pieces (34 problems)
      - Number tables and its properties (13 problems)
      - Tables and tournaments (other) (22 problems)
      - Tournament tables (11 problems)
    - Tournament tables (1 problems)
- Geometry (127 problems)
  - Areas (19 problems)
  - Plane geometry (65 problems)
    - Area (12 problems)
      - Area of a circle, sector, segment (5 problems)
      - Area ratio (3 problems)
        
        Area ratio (other) (1 problems)
      - Finding the area by rearrangment (2 problems)
      - Triangle area (2 problems)
    - Circles (12 problems)
      - Tangent lines and tangent circles (1 problems)
        
        Tangent lines to circles (1 problems)
    - Convex and non-convex figures (2 problems)
      - Convex polygons (2 problems)
    - Geometrical inequalities (1 problems)
      - Triangle inequality (1 problems)
        
        Triangle inequality (other) (1 problems)
    - Locus (1 problems)
      - Locus (other) (1 problems)
    - Polygons (6 problems)
      - Inscribed and circumscribed polygons (1 problems)
      - Polygons (other) (3 problems)
      - Regular polygons (1 problems)
    - Quadrilateral (4 problems)
      - Arbitrary quadrilaterals (1 problems)
      - Circumscribed quadrilaterals (1 problems)
      - Inscribed quadrilaterals (1 problems)
      - Parallelogram (1 problems)
        
        Special cases (1 problems)
        
        Rectangles and squares. Criteria and properties (1 problems)
    - Triangles (24 problems)
      - Similar triangles (14 problems)
      - Types of triangles (6 problems)
        
        Equilateral triangle (2 problems)
        
        Right-angled triangles (4 problems)
        
        Pythagorean theorem and its converse (4 problems)
  - Solid geometry (11 problems)
    - Lines and planes in space (1 problems)
    - Parallelepipeds (3 problems)
      - Special cases of parallelepipeds (3 problems)
        
        Cube (3 problems)
    - Regular polyhedra (1 problems)
      - Main features and definitions of regular polyhedra (1 problems)
    - Skeletons of multifaceted figures (1 problems)
    - Space transformations (1 problems)
      - Projection (1 problems)
        
        Projection helps solve the problem (1 problems)
    - Tetrahedron and pyramid (1 problems)
      - Pyramid (1 problems)
        
        Square pyramid (1 problems)
    - Volume (4 problems)
      - Volume of a parallelepiped (1 problems)
  - Symmetry (21 problems)
- Graph Theory (9 problems)
- Graph theory (30 problems)
- Inequalities (12 problems)
- Mathematical logic (26 problems)
  - Algorithm theory (1 problems)
  - Invariants (1 problems)
- Methods (296 problems)
  - Algebraic methods (32 problems)
    - Counting in two ways (5 problems)
    - Iterations (2 problems)
    - Partitions into pairs and groups; bijections (6 problems)
    - Processes and operations (6 problems)
    - Proof by exhaustion (14 problems)
  - Colouring (25 problems)
    - Chessboard colouring (7 problems)
    - Colouring (other) (3 problems)
  - Examples and counterexamples. Constructive proofs (38 problems)
  - Extremal principle (8 problems)
    - Extremal principle (other) (5 problems)
    - Sorting in increasing (decreasing) order (2 problems)
  - Invariants and semi-invariants (5 problems)
    - Invariants (2 problems)
  - Mathematical induction (32 problems)
    - Mathematical induction (other) (3 problems)
  - Methods from geometry (2 problems)
    - Geometric interpretations in algebra (2 problems)
  - Methods of calculus (1 problems)
    - Continuity considerations (1 problems)
  - Pigeonhole principle (183 problems)
    - Pigeonhole principle (angles and lengths) (10 problems)
    - Pigeonhole principle (area and volume) (6 problems)
    - Pigeonhole principle (finite number of poits, lines etc.) (24 problems)
    - Pigeonhole principle (other) (132 problems)
  - Proof by contradiction (30 problems)
  - Trial and error (2 problems)
- Number theory (2 problems)
  - Numeral systems (1 problems)
- Number Theory (385 problems)
  - Arithmetic operations. Number identities (58 problems)
  - Divisibility (283 problems)
    - Arithmetic functions (4 problems)
    - Divisibility of a number. General properties (52 problems)
    - Divisibility rules (42 problems)
      - Divisibility (1 problems)
      - Divisibility tests for 2 and 4 (3 problems)
      - Divisibility tests for 3 and 9 (16 problems)
      - Divisibility tests (other) (1 problems)
    - Division with remainders. Arithmetic of remainders (61 problems)
      - Arithmetic of remainders (12 problems)
      - Division with remainder (41 problems)
      - Euler's theorem (4 problems)
      - Fermat's little theorem (1 problems)
    - Equations in integer numbers (24 problems)
    - Odd and even numbers (55 problems)
    - Prime numbers (5 problems)
    - Products and factorials (5 problems)
    - The fundamental theorm of arithmetic. Prime factorisation. (10 problems)
    - The greatest common divisor (GCD) and the least common multiplier (LCM). Mutually prime numbers (18 problems)
  - Equations in integer numbers (1 problems)
  - Number theory. Divisibility (1 problems)
    - Division with remainders. Arithmetic of remainders (1 problems)
  - Numeral systems (58 problems)
    - Binary number system (4 problems)
    - Decimal number system (52 problems)
    - Number systems (other) (1 problems)
- Pigeonhole Principle (2 problems)
- Polynomials (1 problems)
  - Invariance principle (1 problems)
- Probability and statistics (97 problems)
  - Probability theory (76 problems)
    - Conditional probability (9 problems)
    - Continuous distribution (4 problems)
    - Discrete distribution (60 problems)
    - Probability theory (other) (9 problems)
  - Statistics (8 problems)
- Puzzles (1 problems)
- Set theory and logic (11 problems)
  - Mathematical logic (2 problems)
  - Theory of algotithms (11 problems)
    - Game theory (11 problems)
- Topology (15 problems)