Simple Colouring

Hard techniques · Updated 4 August 2026

Short answer: pick one shape and find every unit where it has exactly two possible cells. Those pairs link up into a chain. Walk it, marking cells alternately with one of two labels — the chain forces the shape to be all of one label and none of the other. So any cell outside the chain that sees both labels cannot hold that shape at all.

What simple colouring looks like

A unit where a shape has exactly two homes is a strong link: one of the two is right, and exactly one. Chain those links together and you get a network where the shape's positions alternate strictly. Marking alternate cells with two labels is just bookkeeping to keep that alternation straight — it is the alternation, not the marks, that does the work.

Every link joins two cells that are the only homes for the ring in some unit, so the labels must alternate. The struck cell sees a cell of each label, so the ring cannot go there.

The two labels are a note-taking aid on your pencil marks — not how form9 is played. The board itself is solved with shapes, and nothing here depends on the colours in the app.

How to use simple colouring

  1. Pick a shape and find its strong links. Go through the rows, columns and boxes and note every unit where that shape has exactly two possible cells. Each of those is a link — one end of it is right and the other is not.
  2. Build the chain. Join the links that share a cell. A chain of four or more cells is worth marking; anything shorter rarely reaches far enough to eliminate.
  3. Mark alternately. Start anywhere, give that cell one label, and give every cell linked to it the other. Keep going. If you ever have to give one cell both labels, the chain has contradicted itself and the opposite label is solved throughout — a much bigger win.
  4. Strike cells that see both labels. Any cell outside the chain that sees at least one cell of each label cannot hold the shape, because one of those two labels is certainly the shape. Remove it.

This is the entry point to chain solving. The same alternation drives the more advanced chains and loops, and it is also what makes remote pairs work — those are just a chain where every cell happens to hold the same two candidates.

Simple colouring vs X-Wing

Both follow one shape rather than one cell, and an X-Wing is in fact a four-cell colouring chain that closes into a rectangle. The difference is generality: an X-Wing needs the four cells to line up as two rows and two columns, while a chain can take any shape at all as long as each link is a genuine pair. That is why colouring finds eliminations no fish will — but it also asks more of you, because you have to hold the alternation in your head rather than read a rectangle off the grid.

Find Simple Colouring in your own grid

Paste a puzzle and this page will look for Simple Colouring in it — the same pattern shown above, in your grid instead of ours. Nothing is uploaded; it runs in your browser.

Solve the whole puzzle step by step

Frequently asked questions

Is this the same as "simple coloring"?

Yes — same technique, different spelling. This site uses British English throughout, so you will see "colouring" here and "coloring" on many other sudoku sites. Some solvers also call it single-digit colouring or, when the chain closes on itself, a colour trap.

Does this mean form9 is a colour-matching game?

No. form9 is solved entirely with shapes — colour is an optional accessibility reinforcement and off by default. The two labels here are pencil-and-paper bookkeeping for tracking one shape's forced pairs; you could equally use ticks and crosses. Nothing about the technique depends on the app's colours.

What if a cell ends up needing both labels?

That is the jackpot. It means one label leads to a contradiction, so every cell with the other label is that shape — not merely a candidate for it. You go from removing one candidate to placing several shapes at once, which usually finishes the puzzle.

What counts as a strong link?

A unit — row, column or box — where the shape has exactly two possible cells. Exactly two is the whole point: it guarantees one of them is right, which is what makes the alternation valid. Three possible cells is a weak link and cannot carry the chain.