Materials
Open the lesson materials and start learning.
What you will learn
Break an unusual problem apart and look for a familiar pattern inside it
Choose a method that fits the problem instead of relying on one memorised recipe
Write a solution that someone else can follow step by step
Check the result and judge whether it makes sense at all
Who this course is for
Students who are bored
These problems go beyond textbook drills and ask for an idea rather than a procedure.
Competition candidates
Good training ground for contests, where the way you think matters more than arithmetic speed.
Teachers looking for material
Ready-made problems with solutions you can put on the board and take apart with a class.
How to use the materials
Read the lesson
Each lesson takes one topic and explains it from the "why it works" side, with drawings and worked examples. No account needed.
Work the examples yourself
Cover the solution, do it your own way, and only then compare. That is the difference that makes it stick.
Test yourself on exercises
Every curriculum topic has sets of exercises with step-by-step solutions. You can also open a blank PhiBoard and work the problem your own way.
Frequently asked questions
Do the problems come with solutions?
Yes. Every problem includes a full step-by-step solution in the same file.
How hard are they?
From strong secondary-school level up to problems that need a genuine idea, of the kind found at university and in competitions.
Are the materials free?
Yes, they are free to download and need no account.
Can I use them in class?
Yes, you may use them with students. We only ask that you keep the attribution. We are a small independent team in Europe and everything here is free - we want these materials to reach as many people as possible, so if they are useful in your class or among teachers you know, please pass them on.