Maths Olympiad Daily Problems

Art of Problem Solving (AoPS) Problems Categorized by Subject 1. Number Theory: https://artofproblemsolving.com/wiki/index.php/Category:Number_Theory_Problems 2. Geometry: https://artofproblemsolving.com/wiki/index.php/Category:Geometry_Problems 3. Combinatorics: https://artofproblemsolving.com/wiki/index.php/Category:Combinatorics_Problems 4. Algebra: https://artofproblemsolving.com/wiki/index.php/Category:Algebra_Problems Each link provides problems organized into three difficulty levels: 1. Introductory Problems (for those requiring foundational strengthening in the topic) 2. Intermediate Problems (suitable for IOQM qualification, specifically problems 3 through 5) 3. Olympiad Problems (designed for RMO and INMO preparation) Please assess your current proficiency level and commence solving accordingly.

no geometry here in long time

Source: Some USAMO problem

Source: Putnam 1986

Let P be point on side ab in triangle ABC such that AP equal 3pv let Q belongs to C such that aq equal 4 QC prove that BQ bisects a line segment CD

Also complex combinatorics chapter of PFTB by Titu also contains a similar technique on a much advanced level.

https://artofproblemsolving.com/community/c1340h1003741_roots_of_unity_filter?srsltid=AfmBOorqieGq3_0zK4dEaBS31oVc8wpkdvZgYViAr2pv-_zijU6KECtR Roots of unity filter Also read Evan Chen summations handout for more information