4-digit positive number. and simple graph on 4 vertices
Source: 2021 Dürer Math Competition Finals Day2 E6 https://artofproblemsolving.com/community/c2749870_
January 8, 2022
combinatoricsgraph theorygraph
Problem Statement
Bertalan thought about a -digit positive number. Then he draw a simple graph on vertices and wrote the digits of the number to the vertices of the graph in such a way that every vertex received exactly the degree of the vertex. In how many ways could he think about? In a simple graph every edge connects two different vertices, and between two vertices at most one edge can go.