Answer to Question #217636 in Mechanical Engineering for akli

Question

Is it possible to paint the edges of an n-gonal prism with 3 colors so that each face has all 3

colors and all the edges of each vertex have different colors if a)n= 2018; b)n= 2019?

Answer 1

I was able to demonstrate by induction that such coloring is conceivable for divisible by. It turns out to be more practical in this situation to describe the prism as a graph: The colour for the triangular prism is specified explicitly. Then, by induction, it is demonstrated that it is always feasible to color the leftmost edge (in the drawn graph) with color, the rightmost edge with color, and the curve-depicted edges with color. $n3$