Techniques › Simple Colouring
Simple Colouring
Follow one digit's forced chain through the grid in two alternating colours.
Pick a digit. Wherever it has exactly two homes in a house, those two cells form a conjugate pair: exactly one of them is the digit. Chain those pairs together and colour them alternately, and every cell of one colour is true while every cell of the other is false — you just do not yet know which way round.
That is enough for two conclusions. If two cells of the same colour share a house, that colour is impossible, so every cell of it can be cleared. And any cell outside the chain that sees both colours cannot be the digit, whichever way the chain resolves.
Simple Colouring is the gateway to chain logic, and the ideas here — strong links, alternating inference — are the foundation of everything harder.
A worked example
Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.
| 5 | 1 | 2 | 4 | 6 | 7 | 9 | 3 | 8 |
| 4 | 7 | 3 | 8 | 1 | 9 | 2 | 5 | 6 |
| 8 | 9 | 6 | 5 | 3 | 2 | 1 | 4 | 7 |
| 9 | 2 | 8 | 3 | 5 | 1 | 7 | 6 | 4 |
| 3 | 4 | 17 | 6 | 27 | 8 | 5 | 12 | 9 |
| 17 | 6 | 5 | 27 | 9 | 4 | 8 | 12 | 3 |
| 127 | 3 | 17 | 27 | 8 | 6 | 4 | 9 | 5 |
| 6 | 8 | 9 | 1 | 4 | 5 | 3 | 7 | 2 |
| 27 | 5 | 4 | 9 | 27 | 3 | 6 | 8 | 1 |
- NudgeDigit 7 chains across the grid in two alternating colours.
- WhereSimple Colouring in row 7: r5c3, r5c5, r7c3, r6c1, r9c5, r6c4, r9c1, r7c4
- Do itRemove r5c5 ≠ 7, r6c1 ≠ 7, r7c3 ≠ 7, r7c4 ≠ 7, r9c1 ≠ 7
How to spot it
Choose a digit with many conjugate pairs. Start anywhere, colour alternately, and watch for two cells of one colour landing in the same house.
Practise the Simple Colouring →
Where you will meet it
Simple Colouring sits at tier 4 of our ladder, which means it first becomes necessary at Expert. Puzzles below that band never require it, though it may still appear as a shortcut.