Simple Colouring Sudoku Technique Explained

Using colours to track logical chains

Simple Colouring example in Sudoku

What is Simple Colouring?

Simple Colouring is a technique that uses two colours to mark alternating possibilities for a single candidate. By following chains of "conjugate pairs" (cells where a candidate appears exactly twice in a unit), you can identify contradictions or make eliminations.

Think of it as painting cells with two colours – if one colour is "true," the other must be "false."

The Colouring Principle: In a conjugate pair, if one cell contains the candidate, the other cannot (and vice versa). By chaining these relationships, we can track which cells must have opposite states.

Understanding Conjugate Pairs

A conjugate pair exists when a candidate appears in exactly two cells within a unit (row, column, or box). These two cells have a special relationship: one MUST contain the candidate, and the other MUST NOT.

Blue = True

If this cell contains the candidate...

Red = False

...then this cell cannot contain it

How Simple Colouring Works

Step-by-Step Process:

  1. Choose a candidate: Pick a number that appears in several conjugate pairs
  2. Start colouring: Pick any cell with the candidate and colour it Blue
  3. Follow conjugate pairs: The paired cell gets the opposite colour (Red)
  4. Continue the chain: From each coloured cell, find more conjugate pairs and alternate colours
  5. Look for conclusions: Check for contradictions or elimination opportunities

Two Types of Conclusions

Type 1: Colour Contradiction

Two cells of the same colour see each other (share a unit)

Result: That colour is FALSE – eliminate the candidate from ALL cells of that colour

Type 2: Colour Trap

An uncoloured cell sees both colours

Result: Eliminate the candidate from that uncoloured cell

Type 1: Colour Contradiction

Finding a Contradiction

If two Blue cells end up in the same row, column, or box, we have a contradiction. Both cannot be true (a number can't appear twice in a unit).

Conclusion: Blue is false. Remove the candidate from ALL Blue cells.

Bonus: Red must be true – you can place the candidate in all Red cells!

Type 2: Colour Trap

Finding a Trap

If an uncoloured cell can "see" both a Blue cell and a Red cell (shares units with both), the candidate can be eliminated from that cell.

Logic: Either Blue is true OR Red is true. Either way, the uncoloured cell cannot have the candidate.

Building the Colour Chain

Example Chain

  1. Cell R1C3 has candidate 5 – colour it Blue
  2. R1C3 forms a conjugate pair with R1C7 in row 1 – colour R1C7 Red
  3. R1C7 forms a conjugate pair with R4C7 in column 7 – colour R4C7 Blue
  4. R4C7 forms a conjugate pair with R4C2 in row 4 – colour R4C2 Red
  5. Continue until no more connections...

Tips for Success

  • Choose good candidates: Look for numbers with many conjugate pairs across the grid
  • Be systematic: Follow every conjugate pair connection from each coloured cell
  • Check all units: Conjugate pairs can exist in rows, columns, OR boxes
  • Look for both conclusion types: Check for contradictions AND traps
Pro Tip: Simple Colouring works best when a candidate has been significantly reduced through other techniques. The fewer cells containing the candidate, the more likely you'll find useful conjugate pair chains.

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