Objective+6+-+Even+&+Odd+verticies

Question 38**. The question is which of these 4 networks is not traceable, or in simpler terms, which one can you not trace without lifting your pen or going over a path more than once.
 * Here is an example of Even and Odd verticies.

There are two ways to do this question one long way and one short way.

To do this question the long way you would start with the first network and pick on of the verticies and try to trace it following the paths without going over one more than once. You would do this for each of the verticies untill you find one that you cannot trace and that would be your answer. I do not recommend that you use this method, this is what I did when I first started and it doesnt seem to work very well.
 * 1. The long way**

To do the question the short way you first need to become aquainted with Leonard Euler's rules for networks. His theory states that in order for a network to be traceable it must contain either all even verticies or exactly 2 odds and the rest even. Knowing this rule we can now begin to complete this question.
 * 2. The short way**

We all know that a network is a set of points called verticies conected by lines or curves called paths. In order to count the number of odd and even verticies in a network we must first begin with counting the number of paths that are conected to the verticies. In network A we see that there are 3 even verticies and and 2 odd verticies. In network B we see that there are 4 even verticies and 2 odd. In network C we can see that there are 5 even verticies and 2 odd. Lastly in network D we can see that there are 2 even verticies and 4 odd verticies.
 * Step 1 - Count the number of odd or even verticies**

In networks A - C we know that these are traceable beacuse the number of odd verticies in them are exactly two which is the only number they can contain in order to be traceable according to Leonard's rules for networks. We now know, through process of elimination, that network D is the non traceable network because it contains 4 odd verticies, which is two more than allowed in the rules for networks.
 * Step 2 - Determine if the network is traceable**

The answer the the question, "Which of these 4 networks is not traceable" is Network D because it has 4 odd verticies, 2 more than allowed in Leanard Euler's rules for networks.
 * Step 3 - Answer**