
This is an example of adjacent "3" and "3". 


If you mark "x" between them, 


you will have to draw lines around them, making a small loop.
It would be ok if there was no number other than them in the puzzle, but it's impossible. 

Therefore, adjacent "3" and "3" always have a line between them. 

If you mark "x" on this edge, 


then the left "3" will have lines like this, and it makes it clear
where to mark "x" around the two vertices they share.
Now there are two "x" around the right "3", and you cannot draw 3 lines. So you cannot mark "x" on that edge. 

When you draw a line on the left edge of the left "3",
you can also draw a line on the right edge of the right "3" because of symmetric property. 

If you draw a line on top the edge of left "3", 


automatically you can mark "x" on many edges. 

Then there is only one pattern to draw line for the right "3" in this case. 

The other case is when you draw a line on the bottom edge of
the left "3".
There are only these two possiblities for adjacent "3" and "3", so the common part makes another rule. 
Rule of adjacent "3 and 3"  
