- And angles (0 problems)
- Measurement of segments and angles. Adjacent angles. (3 problems)
- Three lines intersecting in the same point (1 problems)

- Measurement of segments and angles. Adjacent angles. (3 problems)
- And secants (0 problems)
- Chords and secants (other) (2 problems)

- Chords and secants (other) (2 problems)
- And skeletons (0 problems)
- Skeletons of multifaceted figures (3 problems)

- Skeletons of multifaceted figures (3 problems)
- Covers and tilings (0 problems)
- Covers (18 problems)
- Dissections with certain properties (8 problems)
- Features of dissection pieces (3 problems)
- Paritions of figures in segments (4 problems)
- Partition rearrangement (2 problems)
- Plane dissected by lines (5 problems)
- Tilings with ordinary and domino tiles (21 problems)
- Various dissection problems (6 problems)

- Covers (18 problems)
- Descriptions (24 problems)
- Empty Category (63 problems)
- Graph theory (27 problems)
- Problems (2367 problems)
- Algebra (41 problems)
- Inequalities (14 problems)

- Inequalities (14 problems)
- Algebra and arithmetics (761 problems)
- Absolute value (5 problems)
- Absolute value of a number (other) (1 problems)
- Equations containing absoute values (1 problems)
- Inequalities containing absolute values (3 problems)

- Absolute value of a number (other) (1 problems)
- Algebra and arithmetics (other) (28 problems)
- Functional equations (11 problems)

- Functional equations (11 problems)
- Algebraic equations and systems of equations (59 problems)
- Algebraic equations and systems of equations (other) (3 problems)
- Binomial theorem (2 problems)
- Diophantine equations (8 problems)
- Higher order equations. Palindromic polynomial equations (37 problems)
- Equations of higher order (other) (37 problems)

- Equations of higher order (other) (37 problems)
- Systems of algebraic non-linear equations (1 problems)
- Systems of linear equations (2 problems)

- Algebraic equations and systems of equations (other) (3 problems)
- Algebraic geometry (6 problems)
- Cryptography (16 problems)
- Number theory (42 problems)
- Binary numerical system (1 problems)
- Divisibility (1 problems)
- Numeral systems (14 problems)

- Binary numerical system (1 problems)

- Number theory (42 problems)

- Cryptography (16 problems)
- Algebraic inequalities and systems of inequalities (22 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)

- Algebraic inequalities (other) (5 problems)
- Arithmetic operations. Number identities (58 problems)
- Arithmetics. Mental maths (62 problems)
- Complex numbers (3 problems)
- Exponential functions and logarithms (6 problems)
- Exponential functions and logarithms (other) (5 problems)
- Exponential inequalities (1 problems)

- Exponential functions and logarithms (other) (5 problems)
- Fractions (3 problems)
- Simple fractions (3 problems)

- Simple fractions (3 problems)
- Graphs and locus of points on the Cartesian plane (18 problems)
- Mean values (55 problems)
- Number systems (57 problems)
- Binary number system (4 problems)
- Decimal number system (51 problems)
- Number systems (other) (1 problems)

- Binary number system (4 problems)
- Number theory. Divisibility (230 problems)
- Arithmetic functions (5 problems)
- Sum and number of divisors of a numberM (4 problems)

- Sum and number of divisors of a numberM (4 problems)
- Divisibility of a number. General properties (53 problems)
- Divisibility rules (42 problems)
- Divisibility tests for 2 and 4 (3 problems)
- Divisibility tests for 3 and 9 (16 problems)
- Divisibility tests (other) (1 problems)

- Divisibility tests for 2 and 4 (3 problems)
- Division with remainders. Arithmetic of remainders (54 problems)
- Arithmetic of remainders (12 problems)
- Division with remainder (32 problems)
- Euler's theorem (4 problems)
- Fermat's little theorem (1 problems)

- Arithmetic of remainders (12 problems)
- Equations in integer numbers (12 problems)
- Number theory. Divisibility (other) (1 problems)
- Odd and even numbers (59 problems)
- Prime numbers (2 problems)
- Products and factorials (4 problems)
- The fundamental theorm of arithmetic. Prime factorisation. (10 problems)
- The greatest common divisor (GCD) and the least common multiplier (LCM). Mutually prime numbers (13 problems)

- Arithmetic functions (5 problems)
- Polynomials (35 problems)
- Algebraic identities for polynomials (12 problems)
- Algebraic identities for polynomials (other) (1 problems)
- Factoring polynomials (6 problems)
- Identical transformations (8 problems)

- Algebraic identities for polynomials (other) (1 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)
- Polynomilas of degree n has not more than n roots (1 problems)
- Quadratic polynomials (11 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)
- Quadratic polynomilal (other) (3 problems)

- Investigating the quadratic polynomial (4 problems)
- Symmetrical polynomials (1 problems)
- Vieta's Formulas (1 problems)

- Algebraic identities for polynomials (12 problems)
- Rational functions (6 problems)
- Inequalities. Method of Intervals. (1 problems)
- Rational equations (2 problems)

- Inequalities. Method of Intervals. (1 problems)
- Sequences (43 problems)
- Progressions (12 problems)
- Arithmetic progression (7 problems)
- Geometric progression (5 problems)

- Arithmetic progression (7 problems)
- Recurrent relations (22 problems)
- Fibonacci numbers (2 problems)
- Linear recurrent relations (6 problems)
- Recurrent relations (other) (14 problems)

- Fibonacci numbers (2 problems)
- Sequnces (5 problems)
- Sums of number sequences and difference series (2 problems)

- Progressions (12 problems)
- Surds. Rational powers. (12 problems)
- Irrational equations. (7 problems)
- Irrational inequalities. (3 problems)
- Square roots. (1 problems)
- Square roots (other) (1 problems)

- Square roots (other) (1 problems)
- Surds. Rational powers (other) (1 problems)

- Irrational equations. (7 problems)
- Trigonometry (18 problems)
- Identical transformations ( trigonomery) (3 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)

- Identical transformations ( trigonomery) (3 problems)
- Word problems (95 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 (70 problems)
- Chessboards and chess pieces (22 problems)
- Number tables and its properties (13 problems)
- Tables and tournaments (other) (23 problems)
- Tournament tables (12 problems)

- Chessboards and chess pieces (22 problems)
- Word problems (other) (3 problems)

- Combined labour (work) problems (1 problems)

- Absolute value (5 problems)
- Arithmetic (5 problems)
- Arithmetic puzzles (3 problems)
- Calculus (221 problems)
- Derivative (27 problems)
- Calculating a derivative (1 problems)
- Convexity and concavity (2 problems)
- Derivative and extrema (2 problems)
- Derivative and multiple roots (12 problems)
- Derivative and tangent line (2 problems)
- Increasing and decreasing. Researching functions (10 problems)

- Calculating a derivative (1 problems)
- Functions of one variable. Continuity (41 problems)
- Certain properties of a function and recurrence relations. (12 problems)
- Continuity and compactness (1 problems)
- Continuous functions (general properties) (4 problems)
- Functions. Continuity (other) (5 problems)
- Intermediate value theorem. Connectedness. (2 problems)
- Monotonicity, boundedness (8 problems)
- Periodicity and aperiodicity (9 problems)

- Certain properties of a function and recurrence relations. (12 problems)
- Functions of several variables (4 problems)
- Integral (3 problems)
- Applications of integration (1 problems)
- Area by integration (1 problems)

- Area by integration (1 problems)
- Calculating integrals (1 problems)
- Existence of a definite integral (1 problems)

- Applications of integration (1 problems)
- Number sequences (31 problems)
- Boundedness, monotonicity (6 problems)
- Limit of a sequence, convergence (12 problems)
- Number e (2 problems)
- Number sequences (other) (11 problems)

- Boundedness, monotonicity (6 problems)
- Real numbers (117 problems)
- Countable and uncountable subsets (1 problems)
- Integer and fractional parts. Archimedean property (87 problems)
- Rational and irrational numbers (30 problems)

- Countable and uncountable subsets (1 problems)

- Derivative (27 problems)
- Combinatorics (226 problems)
- Colorings of the board (15 problems)
- Discrete geometry (other) (3 problems)
- Dissections (20 problems)
- Joke problems (1 problems)

- Joke problems (1 problems)
- Dissections, partitions, covers and tilings (78 problems)
- Dissections (other) (16 problems)

- Dissections (other) (16 problems)
- Euler characteristic (3 problems)
- Geometry on grid paper (12 problems)
- Integer lattices (14 problems)
- Integer lattices (other) (12 problems)
- Polygons and polyhedra with vertices in lattice points (2 problems)

- Integer lattices (other) (12 problems)
- Packing problems (2 problems)
- Painting problems (33 problems)
- Systems of points and line segments (10 problems)
- Center of mass (1 problems)
- Center of mass formula (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)

- Center of mass (1 problems)

- Colorings of the board (15 problems)
- Euclidean geometry (1 problems)
- Examples and counterexamples (3 problems)
- Geometry (401 problems)
- Areas (36 problems)
- Combinatorial geometry (1 problems)
- Eucliden geometry (2 problems)
- Geometry (other) (3 problems)
- Plane geometry (221 problems)
- Area (42 problems)
- Area of a circle, sector, segment (9 problems)
- Area of a parallelogram (3 problems)
- Area of a polygon (2 problems)
- Area of a trapezium (2 problems)
- Area of curvilinear shapes (1 problems)
- Area of quadrilateral (2 problems)
- Area (other) (7 problems)
- Area ratio (8 problems)
- Area ratio of similar figures (1 problems)
- Area ratio of triangles with common base and height (3 problems)
- Area ratio (other) (4 problems)

- Area ratio of similar figures (1 problems)
- Auxiliary area. The area helps solve the problem (1 problems)
- Finding the area by rearrangment (5 problems)
- The area of a composite figure equals to the sum of the areas it is divided into (5 problems)
- Triangle area (5 problems)
- Triangle area (via base and height) (2 problems)

- Triangle area (via base and height) (2 problems)

- Area of a circle, sector, segment (9 problems)
- Circles (33 problems)
- Central angle. Arc length and circumference (5 problems)
- Circle, sector, segment, etc (1 problems)
- Circles (other) (4 problems)
- Connection between the arc length, the angle, and the chord (4 problems)
- Diameter, chords, and secants (2 problems)
- Four points on a circle (2 problems)
- Inscribed angle (10 problems)
- An angle between a secant and a chord (1 problems)
- An angle between two chords or two secants (3 problems)
- Angles supported by congruent arcs and chords (4 problems)
- Inscribed angle (other) (2 problems)

- An angle between a secant and a chord (1 problems)
- Tangent lines and tangent circles (5 problems)
- Tangent circles (2 problems)
- Tangent lines to circles (3 problems)
- Properties and criteria of a secant (1 problems)
- Tangent-secant theorem. Intersecting secant theorem. (1 problems)
- Two tangent lines to a circle, intersecting at a particular point (1 problems)

- Properties and criteria of a secant (1 problems)

- Tangent circles (2 problems)

- Central angle. Arc length and circumference (5 problems)
- Constructions (20 problems)
- Apollonian circles (1 problems)
- Circles (construction) (1 problems)
- Construction of a triangle given different points (2 problems)
- Constructions (other) (6 problems)
- Similar triangles and homothetic transformations (construction) (1 problems)

- Apollonian circles (1 problems)
- Convex and non-convex figures (4 problems)
- Convex polygons (4 problems)

- Convex polygons (4 problems)
- Geometrical inequalities (41 problems)
- Area. A figure lies inside another figure (1 problems)
- Area inequalities (2 problems)
- Geometric inequalities (other) (4 problems)
- Inequalities in a triangle (10 problems)
- A perpendicular distance is the shortest. Ineaqualities for right triangles (1 problems)
- A segment inside the triangle is smaller than the largest side ,Problems (5 problems)
- Inequalities in a triangle involving heights (1 problems)
- Inequalities in a triangle involving medians (1 problems)
- The longest side of the triangle lies opposite the largest angle (2 problems)

- A perpendicular distance is the shortest. Ineaqualities for right triangles (1 problems)
- Polygons (inequalities) (2 problems)
- Quadrilaterals (inequalities) (4 problems)
- The area of a triangle is less than half the product of two sides (1 problems)
- Triangle inequality (18 problems)
- Triangle inequality algebra problems (3 problems)
- Triangle inequality (other) (4 problems)

- Triangle inequality algebra problems (3 problems)

- Area. A figure lies inside another figure (1 problems)
- Lines, segments, rays, and angles (7 problems)
- Lines, segments, rays, and angles (other) (1 problems)

- Lines, segments, rays, and angles (other) (1 problems)
- Locus (8 problems)
- Line or line segment as a locus (1 problems)
- Loci with nonzero area (1 problems)
- Locus and auxiliary triangles (1 problems)
- Locus (other) (5 problems)

- Line or line segment as a locus (1 problems)
- Plane transformations (15 problems)
- Isometry of the plane (3 problems)
- Rotations (3 problems)

- Rotations (3 problems)
- Parallel translation (4 problems)
- Projection onto a line (1 problems)
- Orthogonal projection (1 problems)

- Orthogonal projection (1 problems)
- Similarity (8 problems)

- Isometry of the plane (3 problems)
- Polygons (16 problems)
- Hexagons (1 problems)
- Inscribed and circumscribed polygons (1 problems)
- Pentagons (1 problems)
- Polygons (other) (6 problems)
- Regular polygons (7 problems)
- Sum of internal and external angles of polygons (1 problems)

- Hexagons (1 problems)
- Quadrilateral (14 problems)
- Arbitrary quadrilaterals (1 problems)
- Circumscribed quadrilaterals (1 problems)
- Inscribed quadrilaterals (1 problems)
- Incribed quadrilaterals (other) (1 problems)

- Incribed quadrilaterals (other) (1 problems)
- Parallelogram (9 problems)
- Special cases (8 problems)
- Rectangles and squares. Criteria and properties (8 problems)

- Rectangles and squares. Criteria and properties (8 problems)

- Special cases (8 problems)
- Quadrlaterals (other) (1 problems)
- Trapeziums (1 problems)
- Trapeziums (other) (1 problems)

- Trapeziums (other) (1 problems)

- Arbitrary quadrilaterals (1 problems)
- Triangles (36 problems)
- Incirlce and circumcircle of a triangle (1 problems)
- Relationship of side lengths and angles of a triangle. Solving triangles. (6 problems)
- Ceva's theorem and Menelaus's theorem (1 problems)
- Law of sines (3 problems)
- Relations between sides and angles of a triangle (other) (2 problems)

- Ceva's theorem and Menelaus's theorem (1 problems)
- Remarkable points and lines in a triangle (1 problems)
- Remarkable points and lines in a triangle (other) (1 problems)

- Remarkable points and lines in a triangle (other) (1 problems)
- Similar triangles (5 problems)
- Auxiliary simialr triangles (2 problems)
- Similar triangles (other) (1 problems)
- The triangle generated by bases of two altitudes and a vertex (2 problems)

- Auxiliary simialr triangles (2 problems)
- Sum of angles of a triangle. Exterior angle theorem (2 problems)
- Triangles (other) (6 problems)
- Types of triangles (18 problems)
- Equilateral triangle (4 problems)
- Right-angled triangles (14 problems)
- Pythagorean theorem and its converse (14 problems)

- Pythagorean theorem and its converse (14 problems)

- Equilateral triangle (4 problems)

- Incirlce and circumcircle of a triangle (1 problems)
- Vectors (4 problems)
- Visual geometry (6 problems)

- Area (42 problems)
- Solid geometry (79 problems)
- Convex solids (1 problems)
- Cross-sections, nets, and skeletons (3 problems)
- Lines and planes in space (3 problems)
- Lines and planes in space (other) (2 problems)

- Lines and planes in space (other) (2 problems)
- Parallelepipeds (5 problems)
- Special cases of parallelepipeds (5 problems)
- Cube (5 problems)

- Cube (5 problems)

- Special cases of parallelepipeds (5 problems)
- Polyhedra and polygons in space (1 problems)
- Polyhedra and polygons in space (other) (1 problems)

- Polyhedra and polygons in space (other) (1 problems)
- Regular polyhedra (1 problems)
- Main features and definitions of regular polyhedra (1 problems)

- Main features and definitions of regular polyhedra (1 problems)
- Space transformations (10 problems)
- Isometry (7 problems)
- Isometry helps solve the problem (1 problems)
- Point symmetry (4 problems)
- Reflectional symmetry (5 problems)

- Isometry helps solve the problem (1 problems)
- Projection (2 problems)
- Parallel projection (1 problems)
- Orthographic projection (1 problems)
- Area and orthographic projection (1 problems)

- Area and orthographic projection (1 problems)

- Orthographic projection (1 problems)
- Projection helps solve the problem (1 problems)

- Parallel projection (1 problems)

- Isometry (7 problems)
- Spheres (2 problems)
- Circle on a sphere (2 problems)

- Circle on a sphere (2 problems)
- Tetrahedron and pyramid (2 problems)
- Particular cases of tetrahedra (1 problems)
- Regular tetrahedron (1 problems)

- Regular tetrahedron (1 problems)
- Pyramid (1 problems)
- Square pyramid (1 problems)

- Square pyramid (1 problems)

- Particular cases of tetrahedra (1 problems)
- Visual geometry in space (53 problems)
- Volume (5 problems)
- Ratio of volumes (2 problems)
- Volume of a parallelepiped (1 problems)
- Volume of a prism (1 problems)
- Volume of a tetrahedron and pyramid (1 problems)

- Ratio of volumes (2 problems)

- Convex solids (1 problems)

- Areas (36 problems)
- Grid geometry (1 problems)
- MAthematical logic (1 problems)
- Methods (578 problems)
- Algebraic methods (79 problems)
- Change of variables (0 problems)
- Counting in two ways (21 problems)
- Iterations (5 problems)
- Partitions into pairs and groups; bijections (22 problems)
- Processes and operations (13 problems)
- Proof by exhaustion (20 problems)
- Symmetry and involutions (2 problems)
- Working backwards (1 problems)

- Change of variables (0 problems)
- Colouring (17 problems)
- Chessboard colouring (10 problems)
- Colouring (other) (7 problems)

- Chessboard colouring (10 problems)
- Examples and counterexamples. Constructive proofs (69 problems)
- Extremal principle (18 problems)
- Extremal principle (other) (12 problems)
- Smallest or largest distance (length) (1 problems)
- Sorting in increasing (decreasing) order (4 problems)

- Extremal principle (other) (12 problems)
- Invariants and semi-invariants (32 problems)
- Invariants (38 problems)
- Invariants and semi-invariants (other) (1 problems)

- Invariants (38 problems)
- Mathematical induction (32 problems)
- Mathematical induction in geometry (3 problems)
- Mathematical induction (other) (11 problems)

- Mathematical induction in geometry (3 problems)
- Methods for solving problems with parameter (1 problems)
- Methods from geometry (2 problems)
- Geometric interpretations in algebra (2 problems)

- Geometric interpretations in algebra (2 problems)
- Methods of calculus (3 problems)
- Continuity considerations (2 problems)
- Monotonicity and boundedness (1 problems)

- Continuity considerations (2 problems)
- Pigeonhole principle (395 problems)
- Pigeonhole principle (angles and lengths) (62 problems)
- Pigeonhole principle (area and volume) (13 problems)
- Pigeonhole principle (finite number of poits, lines etc.) (47 problems)
- Pigeonhole principle (other) (249 problems)

- Pigeonhole principle (angles and lengths) (62 problems)
- Proof by contradiction (58 problems)
- Trial and error (2 problems)

- Algebraic methods (79 problems)
- Paintings (1 problems)
- Probability and statistics (143 problems)
- Probability theory (133 problems)
- Conditional probability (21 problems)
- Continuous distribution (12 problems)
- Discrete distribution (101 problems)
- Probability theory (other) (15 problems)

- Conditional probability (21 problems)
- Statistics (10 problems)

- Probability theory (133 problems)
- Set theory and logic (542 problems)
- Joke problem (22 problems)
- Linguistics (3 problems)
- Logic and set theory (35 problems)
- Mathematical logic (326 problems)
- Algorithm theory (1 problems)
- Liars and Knights (1 problems)
- Mathematical logic (other) (136 problems)
- Paradoxes (14 problems)
- Puzzles (54 problems)
- Weightings (2 problems)

- Algorithm theory (1 problems)
- Order relations (10 problems)
- Set theory (18 problems)
- Inclusion-exclusion principle (6 problems)
- Set cardinality. One-to-one correspondence (3 problems)
- Set theory (other) (3 problems)
- Union, intersection, and set difference (4 problems)
- Unusual constructions (3 problems)
- Constructing with right angle (1 problems)

- Constructing with right angle (1 problems)

- Inclusion-exclusion principle (6 problems)
- Theory of algotithms (200 problems)
- Balance puzzles (19 problems)
- Cooperative algorithms (2 problems)
- Game theory (84 problems)
- Fun games (5 problems)
- Game theory (other) (34 problems)
- Symmetric strategies (22 problems)
- Winning and loosing positions (25 problems)

- Fun games (5 problems)
- Theory of algorithms (other) (92 problems)

- Balance puzzles (19 problems)

- Joke problem (22 problems)
- Tilings (1 problems)

- Algebra (41 problems)
- Rotations of homothetic transformations (0 problems)
- A homothetic transformation helps solve the problem (1 problems)
- Homothetic circles (2 problems)

- A homothetic transformation helps solve the problem (1 problems)
- Uncategorized (17 problems)
- Year 2022 (1 problems)