Monthly Archives: August 2025

Count Friends at a Party

Posted on August 15, 2025 by kevin

You are invited by a host at a party with a total of $2025$ people, including the host. Every pair of two people at the party have exactly one common friend. Among them, what is the maximum and minimum number … Continue reading →

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Hyperbolas Covered by a Quadrilateral

Posted on August 2, 2025 by kevin

Four points $A$, $B$, $C$ and $D$ are chosen on each of $4$ hyperbola branches of $x^2y^2=1$ (as $y=\dfrac{1}{x}$ and $y=-\dfrac{1}{x}$ combined). Find the minimum area of the quadrilateral.🔑 Solution: Given that all 4 vertices of the quadrilaterial are on the $4$ branches, let … Continue reading →

Posted in Algebra, Calculus, Geometry | Comments Off on Hyperbolas Covered by a Quadrilateral