Problems and Solutions 

Post 1: This is a problem appeared in ELMO 2025 DAY 1. This is problem 1 in the test. This functional equation is amazing which involves composition of functions. The problem is different because it's not like usual natural looking fuctional equation. Although if the trick once get clicked it is easy to solve the problem. The main crux is the observations and the claims which you will find in the pdf file.

Remark: Download the pdf.(If Interested)

Post 2: This following problem was appeared in International Mathematical Olympiad also known as IMO in the year 2024.This problem is problem 1 in day 1 in IMO 2024. This problem is one of the subset of good problems , I solved in recent one year. I hope you pupils will enjoy the solution and love the problem.

Remark: Download the pdf.(If Interested)

Post 3: Here in this post I had solve an interesting Inequality problem.Most of the inequalites can be solved by AM-GM that is Arithmetic Mean annd Geometric Mean Inequality. The main trick is to understand how to apply that AM-GM optimally. I hope You guys will like this post.

Remark: Download the pdf.(If Interested.)

Post 4: I solved this problem many years back. The following problem is a Diophantine Equation which looks easy at the first glance. However, without proper training it is not possible to tackle the problem with in 2-3 hrs. Although I believe spending about 5-6hrs when you are beginner is a good time count for this problem.The problem involves concept from modular arithmetic and bound properties from idea of inequalities alog with the properties of prime.

Remark: Download the pdf if you wish.