Sector Parity
Each cell has four sectors, one per corner, and the number of them holding exactly one line is always even. Once three of a cell's four sectors are pinned to "exactly one" or "never exactly one", the fourth is settled — even when its own two sides are both still blank.
How it works
- 1Every cell has four sectors, one per corner, and they always hold an EVEN number of =1's — zero, two or four, never one or three. An =1 sector means the loop separates the two cells diagonally across it, and those four relationships close a ring, which cannot disagree with itself an odd number of times.
- 2Read three of the bottom-left cell's sectors straight off the board. Its top-left is =1, because the drawn edge at that border dot needs exactly one partner; its bottom-left is ≠1, because a grid-corner dot has only two edges and can never hold just one; its bottom-right is ≠1, because that border dot's third edge is crossed off.
- 3One =1 so far is odd, so the fourth sector — top-right — must be =1 as well. Notice that both of ITS own sides are still blank: nothing local could have told you this.
- 4That =1 crosses the dot diagonally into the cell above-right, whose sector there has one side already crossed off.
- 5So the other side of it carries the line — draw it.
- Edge on the loop
- Edge the technique adds
- Edge ruled out
- Cells that establish the pattern
- Corner constraint