
The left figure is an examples of corner "2".
Also, when the outside two edges of a vertex around "2" are marked with "x" like the right figure, this is considered as corner "2", too. 


Assume the top edge of "2" is marked with "x". 


Then the three edges around the vertex will be marked with "x".
The total number of "x" around a vertex is always even (also the number of lines around a vertex is always even). 

So, when the top edge of "2" is marked with "x", lines are drawn like this figure. 

On the other hand, if the top edge has a line, the drawing pattern
is as shown in this figure.
These are these two possibilities when the outside edge of a vertex of "2" is blocked with "x". 
Rule of "2" with a blocked vertex  


Here is the example of corner "2".



Let's take a look at bottom left vertex (a) of "2".
Assume the edge below this vertex is marked with "x". 

There are only two possibilities because the top left vertex is blocked.
If the loop goes through the corner, it has to stop at the dead end. 

Even when the loop doesn't go thourgh the corner, it conflicts with the condition. 

Therefore this assumption is wrong. 

For the same reason or the symmetric property, a line can be drawn from the top right vertex of "2" to its right vertex. 
Rule of corner "2"  


This is an example of "2", which is placed on one of the outmost sides of the puzzle and one of its vertices on the outmost side is blocked like this figure. 


Look at bottom left vertex (a) of "2".
Let's take a look from a different point of view this time. 

Lines around this "2" will be drawn from vertex "b" to "a" in either pattern shown in this figure. 

In either case, the line came in from the vertex "b" always goes out from the vertex "a". And since there is no edge on the left side, it has to go down. 
Rule of partly blocked "2"  
