Draw one closed loop through every pearl. A dot is a point where path segments meet. At a white pearl, go straight and turn at the next dot on at least one side. At a black pearl, turn and continue straight through the next dot on both sides.
The black pearl is in the top-left corner, so it can turn only right and down. The black-pearl rule then forces one more straight segment in both directions.
Before: black and white pearls are placed, but no path segments are drawn yet.
After: the black pearl turns right and down. Each arm continues straight through the next dot, and the top arm reaches the white pearl.
Test the whole pearl pattern
Check both next dots for blackFor each possible black turn, make sure both arms can continue straight through the next dot. Cross out a turn that cannot fit both straight exits.Use one side of a white pearl to settle the otherIf the path stays straight at the next dot on one side, it must turn at the next dot on the other side.Let the border remove patternsTest the full rule at a pearl near an edge. A direction is impossible when its required next segment would leave the board.Finish every used dotA dot with one line needs one more exit. After two lines meet there, mark all remaining exits with an X.
Do not join nearby path ends too soon
A short join can close a loop and leave other pearls outside it. Before joining two ends, trace the new loop and make sure every pearl will be on it.