3
Part of 1990 Bundeswettbewerb Mathematik
Problems(2)
172 two-way direct airways between 20 cities
Source: Germany Federal - Bundeswettbewerb Mathematik 1990, round 1, p3
2/21/2020
There are two-way direct airways between cities, at most one between any two cities. Prove that one can reach any city from any other city with at most one transfer.
combinatorics
five nonnegative real numbers with sum 1 around a circle
Source: Germany Federal - Bundeswettbewerb Mathematik 1990, round 2, p3
2/21/2020
Given any five nonnegative real numbers with the sum , show that they can be arranged around a circle in such a way that the five products of two consecutive numbers sum up to at most .
combinatorics