50 challenging problems: equations, logic, and lateral thinking
Fifty advanced problems to tackle with equations, direct reasoning, or lateral thinking, with solutions hidden at first.
ReadMathematics
Articles by topic
Clear, organized learning paths that build strong foundations in mathematics and computer science.
50 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.
ReadPercentages: from meaning to the return to the original value
What % means, how to convert numbers and fractions, how increases and discounts combine, and which percentage reverses a previous change.
ReadAlgorithms: 10 fundamental methods that solve problems
Search, sorting, graphs, dynamic programming, and compression: core idea, pseudocode, complexity, and use cases.
ReadFractions, finally made visible
A concrete way to understand equivalence, sums and proportions.
ReadA 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?
ReadFrom a fraction to a percentage
A path from ratios and equivalent fractions to the idea that a percentage is simply a fraction with denominator 100.
ReadWho occupies the billionth position?
The exact solution to a sequence-position problem in which every natural number n appears exactly n times.
ReadSuccessive percentage changes
How to combine two percentage increases or decreases, why percentages cannot simply be added, and what happens when the two changes are opposites.
ReadThe solution is not enough: Fibonacci’s inheritance
A numerical answer can be correct without explaining why a procedure works. Two problems from the Liber Abaci lead to a proof and a generalisation.
ReadTeaching and learning through problems: from natural language to algebra
A complete teaching pathway for understanding a problem, translating it from natural language into algebra, and choosing strategies such as invariants, divisibility, and working backwards.
ReadPrime numbers and hidden patterns
Divisibility, the sieve of Eratosthenes and regularities that help explore primes.
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