The two-line rule: every cell has either 0 or 2 lines. A cell with one line must get exactly one more; a cell with two lines is full; a cell with only one possible exit can’t be used. Combined with “no premature loops”, this rule resolves most of the board between pearls.
The two-line rule
| Cell state | What it means | Action |
|---|---|---|
| 2 lines | The cell is full. | ✕ its other edges. |
| 1 line, 1 open edge | The line must continue. | Draw the open edge. |
| 0 lines, 1 open edge | The cell can’t be entered and left. | ✕ the last edge (dead end). |
| Pearl with exactly 2 open edges | A pearl must be visited. | Draw both. |
1 Dead ends — and how they cascade
A cell with only one usable edge can’t be on the loop. Crossing out that edge often leaves its neighbour with only one usable edge too, so dead ends spread along corridors.
2 Forced continuations
A line end can never stop. If all but one of its exits are ruled out, draw through the last one. This also chains: the new end may be forced again.
3 Pearls with two exits
A pearl must be visited, so a pearl cell with only two open edges uses both. Here a ✕ on one side of a white pearl rules out the horizontal orientation, so it runs vertically.
4 No premature loops
If the two ends of the same segment are next to each other, joining them closes a loop. Unless that loop already contains every pearl and every line, the edge between them is ✕.
The same idea works at a distance. If a segment’s ends are two cells apart with a single empty cell between them, the loop may not pass through that cell to join them — unless, again, it finishes the puzzle.
The very last connection of every puzzle closes the loop. It’s only allowed when every pearl is on the loop and no other line segment exists.
5 Tracking loose ends
Every partial segment has exactly two ends. On larger boards, keep a mental (or literal) list of which ends belong together. Before joining any two ends, trace the segment from one to the other — if they’re the same segment, the join is premature. This one habit prevents more failed solves than any pattern.
6 Sealed regions
If a group of cells containing a pearl is about to be cut off from the rest of the loop, the loop must enter and leave it. A region with only two possible entrances uses both; a region with one entrance is impossible, so whatever move would create it is wrong. This is the gateway to parity.
Putting it together
After every pearl deduction, sweep the cells around your new lines with the two-line rule, then check every loose end. On Easy and Medium puzzles up to 10×10, alternating pearl techniques with this sweep is enough to finish. Hard puzzles add what-if chains.