Curated Learning
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Follow a continuous path from first puzzles to advanced problem-solving ideas.
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Stage
Primary
Build confidence with visual puzzles, patterns, and first problem-solving habits.
AgesIt is convenient to solve these problems through an equation. The main thing to remember is that the age difference always remains the…Open lessonSums and averagesOpen lessonDivisibilityOpen lessonOlympiad BIDMASOpen lessonCombinatorics (Primary)What is combinatorics? Combinatorics is the branch of mathematics that deals with counting — not just by listing, but by using smart rules…Open lessonCuttingsDivide grid shapes along the lines between cells into a given number of equal parts, or so that each part has exactly one marker.Open lessonFolded-corner perimeterSee why a right-angled notch at the corner of a rectangle does not change the perimeter: inner steps replace exactly what was removed from…Open lessonHow many shapes?Can you spot all the squares, rectangles, and triangles in these diagrams? These classic visual puzzles help develop spatial reasoning,…Open lessonMatchstick EquationsMove one matchstick in a number equation to make it true, or to keep it true.Open lessonTower of HanoiA classic ring-moving puzzle where the move counts 1, 3, 7, 15, 31, ... reveal the beauty of recursion.Open lesson
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Stage
Junior
Connect playful ideas to reusable tactics for early competition problems.
ParityYou, of course, know that there are even and odd numbers.Even numbers are those that are divisible by 2 without a remainder (for example,…Open lessonWorst Case ScenarioOpen lessonRacingOpen lessonEquationsOpen lessonPigeonhole principlePigeonhole Principle (Dirichlet's principle) is a simple, intuitive, and often useful method for proving statements about a finite set.…Open lessonKnights and LiarsThere are two types of inhabitants on the Island of Knights and Liars. Knights always tell the truth. Liars always lie.Open lessonNumber Placement GraphsPlace numbers in circles or cells on a graph while satisfying equal-sum, side-sum, target-answer, or adjacency constraints.Open lessonBase Numbers ProblemsOpen lessonChessboard ColouringClassic board-colouring problems where a simple colour or weight pattern proves an impossibility, or shows the right construction.Open lessonClock — Hours and MinutesExplore clock-hand angle problems: when the hands overlap, point at right angles, or line up in other ways. Touch and drag the clock to set…Open lessonColouringsColour grids, cube faces, vertices, and edges subject to neighbour and count constraints — hands-on entry to construction and proof.Open lessonDoubling the MedianLearn how to apply the method of doubling the median in triangle geometry. Includes proofs and ratio problems involving triangle medians.Open lessonExponents (Last Digit)Explore deep-thinking maths problems involving last digits, powers, prime numbers, and digit tricks. Perfect for ages 11–16 and ideal for…Open lessonKnight ReturnsExact-move knight return problems built around colouring invariants and closed walks in the knight graph.Open lessonMagic SquaresA classic number puzzle where rows, columns, and diagonals all add up to the same magic sum.Open lessonMatchsticks ProblemsMove or remove matchsticks to build target figures with no dangling sticks.Open lessonMaximum Non-Attacking PiecesExtremal chessboard placement problems solved by combining upper bounds with constructions.Open lessonPatterns in Numbers and DigitsProblems on periodicity. Spot patterns in them!Open lessonRatioOpen lessonRiver Crossing RiddlesClassic brain teasers where you transport items or people across a river while following specific rules to avoid dangerous combinations.Open lessonRoman Numeral Matchstick EquationsMove one matchstick in a Roman numeral equation to make it true, or to keep it true.Open lessonRotational SymmetryOpen lessonSquare DissectionsOpen lessonWater Pouring PuzzlesClassic brain teasers where you measure exact amounts using unmarked containers through filling, emptying, and pouring.Open lesson
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Stage
Intermediate
Develop stronger structure, proof habits, and multi-step reasoning.
Axioms and Postulates of EuclidOpen lessonMinimum and Maximum Problems in GeometryMinimum and Maximum Problems in GeometryOpen lessonProductivityOpen lessonFixed Point of a SimilarityInteractive geometry demo: scale, rotate, and drag a shape to see the invariant point appear, then try the guess-the-point challenge mode.Open lessonAM–GM InequalitiesThe Arithmetic–Geometric Mean Inequality:If a ≥ 0, b ≥ 0, then(a + b)/2 ≥ √(ab) ≥ b.Equality holds if and only if a = b.Open lessonBalance Scale PuzzlesClassic counterfeit-coin and balance-scale problems where each weighing splits the cases into three branches.Open lessonChallenging Triangle CongruenceMost students are already familiar with the three standard triangle congruence rules taught in school: SSS (Side-Side-Side), SAS…Open lessonCircumcircle of a TrianglePractice problems on circumcircles of triangles: centers, angles, chords, and construction. Ideal for Olympiad geometry and advanced…Open lessonCryptarithmsWord puzzles where letters represent digits in arithmetic equations. Each letter stands for a unique digit.Open lessonEquations in IntegersSolve equations where the unknowns must be integers. Core techniques: factoring into integer divisor pairs, parity arguments, modular…Open lessonGame Theory & StrategiesIn competitive games, the best outcome depends not only on your own decisions but also on the choices made by others. Strategic thinking…Open lessonGCD and LCMIn this lesson, we will work with the concepts of the greatest common divisor (GCD) and least common multiple (LCM), as well as related…Open lessonInscribed QuadrilateralLearn the theory and solve challenging problems about inscribed quadrilaterals. Perfect for math Olympiad prep, this page covers…Open lessonKnight's TourA chess knight must visit every square exactly once. Explore tours on 5x5 to 8x8 boards and the graph-theory ideas behind them.Open lessonMathematics in ChessAn overview of chessboard problems about parity, move graphs, extremal placements, exact-opponent attacks, and Knight's Tour, with focused…Open lessonNumber TheoryOpen lessonOther Chessboard ProblemsA pair of chessboard construction problems driven by row-column counts and Hamiltonian-style reasoning on custom move graphs.Open lessonPythagoras' theoremThese problems use the Pythagoras theorem and its consequences (perpendicularity criteria, projections, and equal‑tangent loci) to prove…Open lessonRemainders of Squares and CubesOpen lessonSpot the Formula!Recognise and apply standard algebraic identities — difference of squares, square of a sum/difference, sum and difference of cubes, and…Open lessonTangentExplore key theorems about tangents to circles and solve problems involving radii, angles, and geometric constructions with tangents.Open lessonThe Principle of Mathematical InductionMathematical induction is a powerful proof technique for establishing that a statement holds for all natural numbers.Open lessonTriangle InequalityIn this lesson, we will use an important result known as the Triangle Inequality: x + y ≥ x + yOpen lesson
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Stage
Senior
Work through deeper techniques and more abstract olympiad-style thinking.
Exact Opponent AttacksTwo-colour chess placement problems where each piece must attack exactly a fixed number of opponent pieces.Open lessonExtreme PrincipleOpen lessonFlying Rook CyclesA flying rook moves like a rook but each move has length at least 2. Build a Hamiltonian cycle on 4x4 up to 8x8 boards.Open lessonInduction PrincipleThe Induction Principle is of great importance in discrete mathematics: Number Theory, Graph Theory, Enumerative Combinatorics,…Open lessonInvariant PrincipleOpen lessonMaximum and MinimumOpen lessonMethod of ColouringA colouring proof is a sort of invariant proof which can mainly be used to prove that something isn’t possible. The essence of invariant…Open lessonMorley's TriangleOpen lessonSeven Bridges of KönigsbergOpen lesson
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