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Problems Algebra Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property

2.0

In a group of friends, each two people have exactly five common acquaintances. Prove that the number of pairs of friends is divisible by 3.

Problem #PRU-78653

Graph theory Problems Calculus Real numbers Integer and fractional parts. Archimedean property

11–14 2.0

Airlines connect pairs of cities. How can you connect 50 cities with the fewest number of airlines so that from every city you can get to any other city by taking at most two flights?