Key idea: a white pearl is a straight cell that needs a turning neighbour. Because white pearls are straight themselves, they can never supply the turn for each other — which is why groups of white pearls are so powerful.
Rule refresher: white pearl rules.
1 Edge pearls run along the edge
The loop can’t leave the grid, so a white pearl on the border runs parallel to it. (And a white pearl can never be in a corner.)
2 Near-edge pearls running inward are already satisfied
If a white pearl in the second row runs vertically, its upper neighbour sits on the border — where the loop can’t continue upward, so it must turn. The white pearl’s turn rule is automatically met; you only need to finish the cells around it.
3 Edge pairs force turns beyond them
Two adjacent white pearls on the border both run along the edge. Each one’s inner neighbour is the other (straight) pearl, so the loop must turn in the cells just beyond the pair — and on the border, those turns point inward.
4 Rows of three are crossed perpendicular
Three or more white pearls in a line can’t be traversed along the line — the middle one would have no turn. So each is crossed at right angles, giving three parallel lines at once.
5 The far-turn rule
If the loop already goes straight through the cell on one side of a white pearl, the turn must happen on the other side. Mark ✕ to stop the line continuing straight past the pearl.
6 A line approaching a white pair
Two white pearls sit side by side, and a line arrives horizontally one cell short of them. If that line continued into the pair, it would run straight through the approach cell and both pearls — leaving the first pearl with no turn on either side. So the edge into the pair gets ✕, and both pearls must run vertically.
7 White beside black
A black pearl is always a turn. If a black pearl’s arm runs through an adjacent white pearl, that white pearl is satisfied. Conversely, if a white pearl is forced to run the “wrong” way for a neighbouring black pearl, it blocks that arm — see blocked arms.
8 The white-pearl recheck
Each time you draw a line near a white pearl, ask two questions: is its orientation now forced? and is one of its neighbours now forced to go straight? If the answer to the second is yes, the far-turn rule fires immediately.
Practise
White-heavy puzzles are common on 8×8 and 10×10. Combine these patterns with loop logic to finish the regions between pearls.