4
Part of 1975 Bundeswettbewerb Mathematik
Problems(2)
Bundeswettbewerb Mathematik 1975 Problem 1.4
Source: Bundeswettbewerb Mathematik 1975 Round 1
10/22/2022
In the country of Sikinia there are finitely many cities. From each city, exactly three roads go out and each road goes to another Sikinian city. A tourist starts a trip from city and drives according to the following rule: he turns left at the first city, then right at the next city, and so on, alternately. Show that he will eventually return to
combinatoricsgraphcycle
2 brothers inherited n gold pieces of the total weight 2n
Source: 1975 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p4
11/20/2022
Two brothers inherited gold pieces of the total weight . The weights of the pieces are integers, and the heaviest piece is not heavier than all the other pieces together. Show that if is even, the brother can divide the inheritance into two parts of equal weight.
combinatorics