Hello,

I have thought of this math problem I haven't been able to solve, but it must have a simple solution.

We have an undefined (either even or odd) number of line segments and we want to connect their end dots except two of them (for all the set -like if a fluid could get in by the unconnected dot, pass through all the segments and connections and them go out by the other unconnected dot).But there is an imposition: the connection cannot connect two segments that are side by side. Here is an uncompleted sketch

-How can we know wherever it is better to have an odd number of line segments or an even one as to use the less length of connection?

-What is, then, the best disposition of the connections (two by two and then the last one connects with the first one, three by three, etc)?

I guess the way to solve this problem is to create a Cartesian model of it, but I don't know what to do then.

Merry Christmas

Jaime