Draw a single path where each step is a line that goes from the corner of a 1x2 to the opposite corner. Each step must be connected endpoint-to-endpoint to the last. No branching. The path must end on grid walls. The path may touch grid walls or itself without ending; branches being disallowed means that at no point may a step-intersection point be the intersection of three step-lines.
Pearls must not be allowed to see each other in any direction, 360 degrees around, cell center to cell center, with step-lines interrupting line of sight. A pearl that can barely see the corner of a cell is not counted as seeing the pearl in it.
Numbers denote the number of pearls in the region, with a region being any area enclosed completely by step-lines and the walls of the board. There may be multiple same numbers in a region or none at all.
A grey pearl on an intersection point must go on the point where 2 line segments meet. Its number denotes the angle between the two segments, based on the number of cells enclosed by the gap: any intersection where the two lines are going in the same direction will be marked with an 8, because there'll be a 2x4 between the 2 far points. Numberless grey pearls are allowed, marking "this is an intersection".