AUSTRIAN-POLISH 2000 Problem 10
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?
Dataset text AI-MO AoPS. Quoted with source.
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