Shaded pearls mark the start and end points of the path as well as the midpoint, though these might be unmarked.
Unshaded pearls may be placed regularly along the path: one pearl every N steps, where N is the number of unshaded cells on the board rounded to the nearest multiple of 10 (5 is rounded up), divided by 10.
The unshaded pearl count starts from both the start and end point, working toward the middle and stopping when the next unshaded pearl in that direction would cross or sit on the midpoint.
UnshadedShaded
Breaks rule 1: Draw a Hamiltonian path through cell centers.
Breaks rule 3: Shaded pearls mark the start and end points of the path as well as the midpoint, though these might be unmarked.
Breaks rule 4: Unshaded pearls may be placed regularly along the path: one pearl every N steps, where N is the number of unshaded cells on the board rounded to the nearest multiple of 10 (5 is rounded up), divided by 10.