20 logic puzzles: liars, jobs and paradoxes
Twenty puzzles with hidden solutions: truth-tellers and liars, six four-person job matchings, and six paradoxes to discuss.
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Clear, organized learning paths that build strong foundations in mathematics and computer science.
Logic
A curious situation involving ages
An algebraic logic problem about age gaps among three siblings: why can the situation occur only when the gaps are consecutive numbers?
Read50 challenging problems: equations, logic, and lateral thinking
Fifty advanced problems to tackle with equations, direct reasoning, or lateral thinking, with solutions hidden at first.
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Algebra
A 4×4 magic square with your chosen sum
Two constructions for a 4×4 magic square with any integer sum: the formula 21a+b and a transformation of the normal square with sum 34.
ReadBaker’s transformation: chaos that mixes images
Stretch, compress and reassemble: use images and points to see how a deterministic rule produces surprising mixing.
ReadFast mental calculation: recognize the structure before calculating
Eighteen explained techniques and their identities, 25 problems and an interactive practice laboratory.
ReadSix Kordemsky puzzles: with and without algebra
Six classic puzzles approached first through insight and then checked mathematically: coins, apples, averages, a current and two meetings.
ReadNotable sums: from Gauss to even and odd numbers
A chain of formulas born from one idea: pair the extremes, then transform the sum of natural numbers into sums of evens and odds.
ReadTen very challenging linear and quadratic word problems
Five reworked classics and five newly framed problems, with equations, constraints, rejected roots and step-by-step checks.
ReadThe same problem, different mathematics: from intuition to parameters
Eight situations explored in primary, lower-secondary, and upper-secondary terms: an advanced model helps the teacher design concrete explanations without imposing it on the child.
Read50 challenging linear word problems with solutions
Fifty challenging real-world problems solvable with first-degree equations. Solutions are hidden and, when useful, include a method without an equation.
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Number theory
Linear Diophantine equations: a general method using extended Euclid
Solve ax + by = c without guessing: theory and example side by side, Bézout’s identity, every integer solution and non-negativity constraints. With a step-by-step laboratory.
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