MathDB

3

Part of 2016 Czech-Polish-Slovak Junior Match

Problems(2)

assign pairwise different positive integers to vertices of n-gonal prism

Source: Czech-Polish-Slovak Junior Match 2016, individual p3 CPSJ

1/20/2020
Find all integers n≥3n \ge 3 with the following property: it is possible to assign pairwise different positive integers to the vertices of an nn-gonal prism in such a way that vertices with labels aa and bb are connected by an edge if and only if a∣ba | b or b∣ab | a.
Poland
combinatorial geometrycombinatoricsdividesgeometry3D geometryprism
each lines of a set in a plane intersects exactly 15 other lines

Source: Czech-Polish-Slovak Junior Match 2016, team p3 CPSJ

1/20/2020
On a plane several straight lines are drawn in such a way that each of them intersects exactly 1515 other lines. How many lines are drawn on the plane? Find all possibilities and justify your answer.
Poland
combinatoricscombinatorial geometry