Curated Learning
Library
Follow a continuous path from first puzzles to advanced problem-solving ideas.
Learning path
Work through the stages in order, or jump to the point that fits you now.
Stage
Primary
Build confidence with visual puzzles, patterns, and first problem-solving habits.
CuttingsDivide grid shapes along the lines between cells into a given number of equal parts, or so that each part has exactly one marker.Folded-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…Matchstick EquationsMove one matchstick in a number equation to make it true, or to keep it true.Tower of HanoiA classic ring-moving puzzle where the move counts 1, 3, 7, 15, 31, ... reveal the beauty of recursion.
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Stage
Junior
Connect playful ideas to reusable tactics for early competition problems.
Number Placement GraphsPlace numbers in circles or cells on a graph while satisfying equal-sum, side-sum, target-answer, or adjacency constraints.Chessboard ColouringClassic board-colouring problems where a simple colour or weight pattern proves an impossibility, or shows the right construction.Clock — 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…ColouringsColour grids, cube faces, vertices, and edges subject to neighbour and count constraints — hands-on entry to construction and proof.Column Arithmetic RestorationRestore damaged column calculations by finding the missing digits in addition, subtraction, and multiplication records.Divisibility by 11Alternating digit-sum rule and a proof exercise.Divisibility by 2 and 4Quick tests using the last one or two digits; practice with interactive digit-placement puzzles.Divisibility by 3 and 9Digit-sum rules and puzzles that build fluency with multiples of 3 and 9.Divisibility by 5 and 10Last-digit tests for 5 and 10, with interactive fill-in puzzles.Doubling the MedianLearn how to apply the method of doubling the median in triangle geometry. Includes proofs and ratio problems involving triangle medians.Knight ReturnsExact-move knight return problems built around colouring invariants and closed walks in the knight graph.Magic SquaresA classic number puzzle where rows, columns, and diagonals all add up to the same magic sum.Matchsticks ProblemsMove or remove matchsticks to build target figures with no dangling sticks.Maximum Non-Attacking PiecesExtremal chessboard placement problems solved by combining upper bounds with constructions.River Crossing RiddlesClassic brain teasers where you transport items or people across a river while following specific rules to avoid dangerous combinations.Roman Numeral Matchstick EquationsMove one matchstick in a Roman numeral equation to make it true, or to keep it true.Water Pouring PuzzlesClassic brain teasers where you measure exact amounts using unmarked containers through filling, emptying, and pouring.
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Stage
Intermediate
Develop stronger structure, proof habits, and multi-step reasoning.
Fixed 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.Balance Scale PuzzlesClassic counterfeit-coin and balance-scale problems where each weighing splits the cases into three branches.CryptarithmsWord puzzles where letters represent digits in arithmetic equations. Each letter stands for a unique digit.Equations in IntegersSolve equations where the unknowns must be integers. Core techniques: factoring into integer divisor pairs, parity arguments, modular…Game Theory & StrategiesIn competitive games, the best outcome depends not only on your own decisions but also on the choices made by others. Strategic thinking…Knight's TourA chess knight must visit every square exactly once. Explore tours on 5x5 to 8x8 boards and the graph-theory ideas behind them.Mathematics in ChessAn overview of chessboard problems about parity, move graphs, extremal placements, exact-opponent attacks, and Knight's Tour, with focused…Other Chessboard ProblemsA pair of chessboard construction problems driven by row-column counts and Hamiltonian-style reasoning on custom move graphs.Spot the Formula!Recognise and apply standard algebraic identities — difference of squares, square of a sum/difference, sum and difference of cubes, and…The Principle of Mathematical InductionMathematical induction is a powerful proof technique for establishing that a statement holds for all natural numbers.
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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.Flying 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.
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