Hat House

Gokigen Puzzle Challenge Hat House

Gokigen is played on a rectangular grid in which numbers in circles appear at some of the intersections on the grid. The object is to draw diagonal lines in each cell of the grid, such that the number in each circle equals the number of lines extending from that circle. Additionally, it is forbidden for the diagonal lines to form an enclosed loop. As a direct consequence of the rules, all diagonal lines must be connected to the edges of the grid by other such lines. If not, one would immediately create a closed circuit around this line. Therefore, if a network of lines does not touch the edge of the grid, and only has one place where it can touch the edge, then it must do so.