Sector Chain
Hard
Used by Smart Hint
A sector is the pair of a cell's sides meeting at one of its corners, and the loop uses 0, 1, or 2 of them. A 2 passes the same count to its opposite corner, and every dot passes it on diagonally, so the fact travels along a whole chain of sectors. A chain seeded at a border or a 3 forces edges far from where it started.
- Edge the technique adds
- Cells that establish the pattern
- Corner constraint
How it works
- A SECTOR is the pair of a cell's sides that meet at one of its corners. The loop uses 0, 1, or 2 of them, and you can jot down what you've ruled out with the =1 / ≠1 / ≠2 / ≠0 marks.
- Watch how a 2 treats its sectors: whatever count one uses, the OPPOSITE sector must make up the rest — so a 2 with exactly one line in a sector has exactly one line in the opposite sector too.
- At the dot between two diagonal cells, their two sectors together make up all four of the dot's edges — and every dot carries 0 or 2 lines. So "exactly one" crosses the dot into the next diagonal cell unchanged.
- Put those together and a diagonal run of 2s becomes a wire: a fact entering one end travels the whole chain, no matter how long it is. That's the =1 marks running down the middle here.
- The top 3 can't put all of its lines in one sector pair — so its inner sector carries at least one line, and that fact travels down the chain of 2s to the far 3.
- A 3 receiving "exactly one" at its inner sector must put its other two lines on the outer one: both outer edges of BOTH 3s are forced, even though the two clues are nowhere near each other.