One unbroken loop, drawn between the dots, and every number tells you exactly how many of its sides the loop must use.
Connect dots with horizontal and vertical segments to form a single closed loop that never crosses or branches. Each numbered cell must be surrounded by exactly that many edges of the loop; cells without a number can have any count. There's one solution, reachable by pure logic.
Known in Japan as Slitherlink, this is an original puzzle of Nikoli — not a folk form they popularised, but one their magazine created. It first appeared in Puzzle Communication Nikoli #26 in June 1989.
It was assembled rather than invented in one go: the editor combined two separate puzzles readers had contributed. The first version was also stricter and stranger than the modern one — every square carried a number, and the edges were not required to close into a loop.
Dropping both of those constraints is what made it good. Most squares now say nothing at all, and the single closed loop becomes the thing you are solving for, so the empty regions carry as much information as the numbered ones.
Fences is the classic single-loop logic puzzle, rebuilt as an original, solver-verified free browser game with multiple difficulties and a daily challenge.