Kurotto and Juosan are Nikoli's pencil puzzles. We study the computational complexity of Kurotto and Juosan puzzles. It is shown that deciding whether a given instance of each puzzle has a solution is NP-complete.

The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. The chromatic art gallery problem is to find a guard set for P such that no two guards with the same color have overlapping visibility regions. We study the decision version of this problem for orthogonal polygons with r-visibility when the number of colors is k=2. Here, two points are r-visible if the smallest axis-aligned rectangle containing them lies entirely within the polygon. In this paper, it is shown that determining whether there is an r-visibility guard set for an orthogonal polygon with holes such that no two guards with the same color have overlapping visibility regions is NP-hard when the number of colors is k=2.

Herugolf and Makaro are Nikoli's pencil puzzles. We study the computational complexity of Herugolf and Makaro puzzles. It is shown that deciding whether a given instance of each puzzle has a solution is NP-complete.

The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. A chromatic guarding is said to be conflict-free if at least one of the colors seen by every point in P is unique (i.e., each point in P is seen by some guard whose color appears exactly once among the guards visible to that point). In this paper, we consider vertex-to-point guarding, where the guards are placed on vertices of P, and they observe every point of the interior of P. The vertex-to-point conflict-free chromatic art gallery problem is to find a colored-guard set such that (i) guards are placed on P's vertices, and (ii) any point in P can see a guard of a unique color among all the visible guards. In this paper, it is shown that determining whether there exists a conflict-free chromatic vertex-guard set for a polygon with holes is NP-hard when the number of colors is k=2.