Yajilin is a puzzle originally from nikoli; you can see their description of the puzzle here. Some cells contain a number and arrow. The object is to fill in some of the empty cells so that each number indicates how many filled cells its corresponding arrow points to. No two filled cells may be adjacent. Finally, the remaining cells must all be connected to form a single closed loop that passes through each empty cell once. Both the configuration of filled cells and the closed loop are unique.
Below is an example puzzle and its only solution.