Try this beautiful problem from PRMO, 2019, Problem 18 based on Ordered Pairs. Orderd Pairs | PRMO | Problem-18 How many ordered pairs \((a, b)\) of positive integers with \(a < b\) and \(100 \leq a\), \(b \leq 1000\) satisfy \(gcd (a, b) : lcm (a, b) = 1 : 495\) ?...

Try this beautiful problem from Geometry based on Circular Cylinder. Circular Cylinder Problem – AMC-10A, 2001- Problem 21 A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter $10$ and...

Try this beautiful problem from Geometry: Area of the region Problem on Area of the Region – AMC-10A, 2007- Problem 24 Circle centered at \(A\) and \(B\) each have radius \(2\), as shown. Point \(O\) is the midpoint of \(\overline{AB}\), and \(OA = 2\sqrt {2}\)....

Try this beautiful problem from Geometry based on Circumscribed Circle Problem on Circumscribed Circle – AMC-10A, 2003- Problem 17 The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its...

Try this beautiful problem from Algebra based on Sum of the digits. Sum of the digits – AMC-10A, 2007- Problem 25 For each positive integer $n$ , let $S(n)$ denote the sum of the digits of $n.$ For how many values of $n$ is \(n+s(n)+s(s(n))=2007\)...

Try this beautiful problem from Geometry based on medians of triangle Medians of triangle | PRMO | Problem 10 In a triangle ABC, the medians from B to CA is perpendicular to the median from C to AB. If the median from A to BC is 30,determine \((BC^2 +AC^2+AB^2)/100\)?...