This question maybe ridiculous but I always found it interesting... Here it is : (I cannot put image so I put you the link of the pictures) When I was in school I used to draw houses when I was bored :
You can draw it without lifting the pen. But then I tried to draw two houses side-to-side :
Then I realized you cannot actually do it without lifting the pen. I tried any ways I could. You end up all the time with one line missing.
That's why I was wondering whether there existed a proof that I cannot actually do it.
I heard that we have to count the total number of lines and the number of intersections and that this number tells us something but I am not sure at all.
I am a first year maths student so I haven't studied graph theory yet !