If you've ever stared at a hard Sudoku grid knowing that the answer must be in there somewhere but unable to see it, colour-based solving techniques might be exactly what you need. Simple Colouring — also called Conjugate Pairs colouring — is one of the most visually intuitive methods for cracking puzzles that have defeated every other approach. It turns the abstract relationships between candidates into a literal picture on the grid, making connections visible that are nearly impossible to spot through pure logical analysis.
What a Conjugate Pair Is
A conjugate pair is a pair of cells in the same unit (row, column, or box) where a specific candidate digit appears in exactly two cells. Because the digit must appear exactly once in that unit, and there are only two options, these cells have a rigid relationship: if one is the solution, the other cannot be, and vice versa. They are linked in an either-or relationship that Simple Colouring exploits.
How Simple Colouring Works
Choose a candidate digit that you want to work with — ideally one that appears in many conjugate pairs across the grid. Pick any conjugate pair and assign one cell Colour A (say, blue) and the other Colour B (orange). Now look for other conjugate pairs that include one of those coloured cells. The new partner cell gets the opposite colour. Continue chaining: blue connects to orange, orange connects to blue, through every linked conjugate pair in the grid.
Row 2 has 5 only in C3 and C7 → C3 = Blue, C7 = Orange
Column 7 has 5 only in R2 and R8 → C7 is Orange, so R8C7 = Blue
Box 9 has 5 only in R8C7 and R9C9 → R8C7 is Blue, so R9C9 = Orange
Chain: C3(B) — C7(O) — R8C7(B) — R9C9(O)
Once you've coloured every reachable cell in the chain, you have two competing hypotheses: either all the Blue cells are correct (and all Orange cells are wrong), or all the Orange cells are correct (and all Blue cells are wrong). Only one hypothesis can be right.
Making Eliminations
Simple Colouring produces two types of useful results. The first is a contradiction within a colour: if two Blue cells see each other (share a row, column, or box), they can't both be correct — so the Blue hypothesis is impossible, and all Orange cells must be the solution. Place all Orange cells immediately.
The second result is an external elimination: if a cell outside the chain contains the candidate digit and can see both a Blue cell and an Orange cell, it cannot be the solution regardless of which hypothesis is correct. Either the Blue or Orange cell in its view will be placed, eliminating this cell in both scenarios. Remove the candidate from this external cell.
Digital vs. Paper Colouring
Most Sudoku apps support colour-marking of candidates directly — usually accessible by long-pressing or right-clicking a candidate. This makes Simple Colouring fast and clean. On paper, use two different coloured pencils or simply mark one colour with a circle around the candidate number and the other with a square. The notation matters less than the consistency — as long as you can clearly see which cells belong to which hypothesis, the technique works.
Simple Colouring is the entry point to a family of more advanced techniques including Multi-Colouring and 3D Medusa, which extend the same visual chain logic to multiple digits simultaneously. Mastering Simple Colouring first gives you the visual intuition to tackle those more complex variants when the time comes.