Königsberg had seven bridges connecting two islands and two riverbanks. People asked: can you walk a route that crosses every bridge exactly once? Euler proved you can't.
Why not
If a path enters and leaves a place an equal number of times, the bridges connecting it must be even (entrance + exit pairs). All four landmasses had odd numbers of bridges. So no — impossible.
This is the founding problem of graph theory. Euler invented a whole branch of maths to answer 'can I walk this?'.