Draw a single loop that goes through every node exactly once. At bridges, the line is allowed to cross itself.
The circular shaped nodes in the corners and the node directly above the node in the lowerright corner all have only two exits and because the line passes through it, they must all be used.
Now we see that in doing that the middle node at the bottom row was made part of our loop already. Because therefore the path from there to above will not be used, for the node directly above it only two paths remain and should be used.
If we would connect the node above the node in the lowerleft corner to the node neighbouring on the right, we would create a loop that does not contain every node in the puzzle, so it has to be connected with his neighbour above. As soon as we connect the two loose ends in the trivial way, we finished the puzzle.
This genre was named after the Irish mathematician Sir William Rowan Hamilton who was once looking for a closed path on the edges of a dodecahedron while visiting every corner exactly once. More generally, nowadays we call such a path a Hamiltonian cycle.
Puzzles in this genre