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Sudoku techniques · Expert

Simple Coloring in Sudoku

Simple Coloring follows one number's strong links from cell to cell and paints them in two alternating colours. Exactly one colour is true and the other is false. Two consequences follow: any uncoloured cell that sees both colours cannot hold the number, and if two cells of the same colour see each other, that whole colour is false.

Also known as: Singles Chains.

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Why it works

Coloring a chain of strong links splits it into two colors, one true and one false. An uncolored cell seeing both colors loses that candidate, and if two cells of one color see each other, that color is false.

How to spot it

Pick a number that is short on places: one that has exactly two spots in several units.

  • Start anywhere, colour it A, colour its strong-link partner B, and keep alternating along every link you can follow.
  • Stop and check two things: a cell seeing both colours, and two same-coloured cells sharing a unit.
  • The second case is the more powerful one: it settles the entire chain at once.

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Worked example

These are the app's own lesson boards. Step through them the same way a hint does.

PatternAnswerContextBlockerElimination
Step 1 of 2
Simple Coloring: the pattern as the app draws it during a hint.
  1. 1

    Building a chain of conjugate pairs (strong links) for 4: each link joins a cell and a cell that are the only two cells for 4 in one row, column, or box.

  2. 2

    One color must be true, so we can remove the candidate 4 from any uncolored cell that sees both colors .

Where it fits

The game looks for the easiest technique that applies before it offers you a harder one. Simple Coloring sits at position 18 of 37 on that ladder, which is why puzzles that need it are graded Expert.

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