plan of castle in Baranow Sandomierski as a graph with 16 vertices
Source: Austrian - Polish 2000 APMC
May 4, 2020
combinatorial geometrycombinatorics
Problem Statement
The plan of the castle in Baranow Sandomierski can be presented as the graph with vertices on the picture.
A night guard plans a closed round along the edges of this graph.
(a) How many rounds passing through each vertex exactly once are there? The directions are irrelevant.
(b) How many non-selfintersecting rounds (taking directions into account) containing each edge of the graph exactly once are there?
https://cdn.artofproblemsolving.com/attachments/1/f/27ca05fc689fd8d873130db9d8cc52acf49bb4.png