Crossing Parity
The loop is closed, so any straight line drawn across the whole board crosses it an even number of times. When every crossing edge in a row or column is decided but one, that last edge is forced — whatever makes the count even.
How it works
- 1The finished loop is one closed shape — so a straight line drawn across the WHOLE board must cross it an even number of times. Zero, two, four… never an odd count.
- 2Look at the middle row here: its four crossing edges are the four vertical edges along it, and a full left-to-right sweep crosses the loop once for each of them that's a line.
- 3Three of the four are already decided — one line, two X's. That's one crossing so far: an odd count.
- 4The last crossing edge must make the total even, so it's forced to be a line. (Had the count already been even, it would be forced to an X instead.)
- 5This works on any full row or column, any time exactly one of its crossing edges is still undecided — no clues needed at all.
- Edge on the loop
- Edge the technique adds
- Edge ruled out
- Cells that establish the pattern