Region Coloring

Expert Used by Smart Hint

Shading every cell as inside or outside the loop (with the space beyond the grid always outside): a line always separates two different shades, a blank always keeps the same shade. Chaining that logic across the board pins down edges too far apart for any single clue to reach alone.

Edge on the loop
Edge ruled out
Inside / outside the loop

How it works

The loop always splits the whole board into exactly two regions — inside and outside. Shade every cell as you learn which region it's in.
A blank edge between two cells means they're the SAME region — the left and middle cells here share a blank edge, so they're shaded the same color.
A line between two cells means they're DIFFERENT regions — the middle and right cells share a line, so the right cell gets the other color.
The left and right cells aren't directly next to each other, but we now know for certain they're in different regions too — that's the power of this technique: it reaches conclusions ordinary adjacent-clue checking can't, by chaining through cells that are already colored.
Once two cells are both colored, ANY edge between them is settled immediately: same color means blank, different colors means line — no clue-counting needed at all.