Problem #PRU-30820

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
 12–14  2.0

Problem

In some country there is a capital and another 100 cities. Some cities (including the capital) are connected by one-way roads. From each non-capital city 20 roads emerge, and 21 roads enter each such city. Prove that you cannot travel to the capital from any city.