Try this beautiful Problem on Graph Coordinates from coordinate geometry from AMC 10A, 2015. Graph Coordinates – AMC-10A, 2015- Problem 12 Points $(\sqrt{\pi}, a)$ and $(\sqrt{\pi}, b)$ are distinct points on the graph of $y^{2}+x^{4}=2 x^{2} y+1 .$ What is...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Length and Triangle. Length and Triangle – AIME I, 1987 Triangle ABC has right angle at B, and contains a point P for which PA=10, PB=6, and \(\angle...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Algebra and Positive Integer. Algebra and Positive Integer – AIME I, 1987 What is the largest positive integer n for which there is a unique integer k such...

Try this beautiful Positive Integer Problem from Algebra from PRMO 2017, Question 1. Positive Integer – PRMO 2017, Question 1 How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Distance and Spheres. Distance and Sphere – AIME I, 1987 What is the largest possible distance between two points, one on the sphere of radius 19 with...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2015 based on Arithmetic Mean. Arithmetic Mean of Number Theory – AIME 2015 Consider all 1000-element subsets of the set {1, 2, 3, … , 2015}. From each such subset choose...