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Sudoku Simple Colouring

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.