Plumber

Pipe segments of assorted shapes lie scattered across a grid, each able to rotate a quarter turn at a time. The task is to line their ends up into one continuous run from the source to the outlet. Finish and the water flows through to show whether the route really connects.

The trap is that the shortest-looking path is seldom the one that works, because the pieces already sitting in each square constrain what shape the route can take. Working forward from the source alone usually dead-ends halfway. People who solve these quickly work backwards from the outlet at the same time.

Another habit that helps is leaving uncertain pieces alone at first. Scan the whole board for segments that have only one possible orientation and start there. Each of those forces its neighbours a little further, until the full route reveals itself without much guesswork.