Paint the digit's either-or chain in two colours → erase the side that contradicts itself.
Technique 12 in the order the hint searches · difficultyExpert · up to advanced techniques
If a 3 has exactly two homes in some unit, those two cells are bound together as “if one is right the other is wrong”. Follow links like that, alternating colours, and a two-coloured chain grows across the grid.
Follow the places where a digit has exactly two homes
Fix on one digit and find units — rows, columns or boxes — where it has exactly two possible cells. Join those two and paint them differently. Keep going and the chain crosses the grid; around four cells in, it starts being worth something.
This is how the hint puts it
Following the places where 3 has just two homes and painting them in two colours, the same colour turned up twice in column 4 — at r4c4 and r8c4. One column cannot hold two 3s, so that colour is wrong outright and 3 comes off every cell of it.
One colour is entirely right and the other entirely wrong
Cells joined by the chain share a fate if they share a colour. That gives two conclusions: if the same colour appears twice in one unit, that colour is wrong outright; and any cell that sees both colours cannot be that digit whichever side turns out to be right.
The first technique that uses a chain. Where the earlier ones finish inside a single unit, this one runs clear across the grid.
Puzzles where this technique decides it
Four puzzles that won't give up the next move until you reach Simple Colouring. Press a number to open it.
- Practice 1 ·
4-6586742 - Practice 2 ·
4-3201308 - Practice 3 ·
4-2072830 - Practice 4 ·
4-7687396