Olympiad Combinatorics practice
Four combinatorics problems for practice. The first two problems are on invariants, the third problem uses intermediate value theorem and the last one is a game.
Four combinatorics problems for practice. The first two problems are on invariants, the third problem uses intermediate value theorem and the last one is a game.
This post contains a unique mix of geometry problems with diverse techniques: Angle chasing, power of a point, complex numbers, inversion and Euclidean transformations. The solutions of some of these problems are not available elsewhere in the internet. I believe that since I tried searching a lot before rolling my sleeves and attempting them. I used this set in INMO training camp 2024-25 at Bangalore, Bhopal and Chennai. Enjoy!
I solved the RMO problems today after the exam. I am documenting the solutions and my feelings of difficulty (out of 5) for each problem. I hope you enjoy the solutions. Let me know if you liked it, and share the solutions with interested people.