Bag (puzzle)

Bag, also published under the names Corral and Cave, is a logic puzzle created by the Japanese puzzle publisher Nikoli, played on a grid of cells in which some cells contain a number. The solver draws a single continuous, non-branching loop through the grid so that each numbered cell ends up outside the loop, with the number stating exactly how many empty cells can be seen from that cell looking in the four orthogonal directions before the loop or the edge of the grid blocks the view, counting the numbered cell itself as one of them. Every unnumbered cell must end up either fully enclosed by the loop or fully outside it, and the loop itself may not touch or cross itself at any point. As with Nikoli's other pencil puzzles, the appeal lies in reasoning out a single valid loop from the placement of the number clues alone, using elimination rather than guesswork.