Math Olympiad - Problems And Solutions

You learn to prove why things work, not just that they work.

of problems in major competitions like the IMO (International Mathematical Olympiad). Study Guide: A structured collection of practice problems and step-by-step solutions math olympiad problems and solutions

We can test it for small numbers: $1 = 1^2$ $1 + 3 = 4 = 2^2$ $1 + 3 + 5 = 9 = 3^2$ It looks true. But checking examples is not a proof. You learn to prove why things work, not just that they work