Quick! Draw a path which intersects every
line exactly once. An Eulerian trail is a path which visits every edge exactly once.
But if your smug puzzle-giver has presented it as: “draw a path which intersects every
line exactly once,” you can seize this opportunity to be technically correct. Here is one example.
A vertex of two line segments is technically one point on two different lines, an edge
however does not include the vertex. Here is another example. Fun fact: if three or
more lines intersect at one point they are said to be concurrent.