A conjugate pair is two cells in the same house that are the only cells containing a particular candidate. Whichever cell is wrong, the other must be right - making conjugate pairs the strongest possible logical link.
A conjugate pair is the strictest form of "two cells, two possibilities" in Sudoku. When a candidate has exactly two viable cells inside a single house, those two cells form a conjugate pair for that digit. One of them must hold the digit; the other cannot.
The relationship is symmetric: knowing either cell's truth determines the other. This kind of strict either/or relationship is called a strong link, and it is the building block of every chain technique.
Conjugate pairs let you reason "if A then not B, if not A then B" with absolute certainty. That binary structure is what powers Coloring: paint one cell of the pair color X and the other color Y, then propagate along more pairs until two cells of the same color see each other - which is impossible, proving every cell of that color is wrong.
They are also the strong-link half of every chain. A chain alternates strong (conjugate-pair) links with weak (shared-house) links. Without conjugate pairs you cannot build a chain at all.
Pick any digit. Scan each row, column, and box. Wherever the digit has only two candidate cells, you've found a conjugate pair. With full pencil marks, this becomes a one-pass exercise per digit.
Once spotted, the pair becomes a tool: feed it into Coloring, an X-Wing, or an X-Chain. See the glossary for related strong-link patterns.
No. A naked pair is two cells in a house that share the same two candidates. A conjugate pair is two cells in a house that are the only places a single candidate can go. They are different patterns and serve different purposes.
Yes. The same cell can be in a conjugate pair in its row for digit 4, in its column for digit 7, and in its box for digit 9. That's how chains thread through the grid.
Because the relationship is total: exactly one of the two cells holds the digit. Other cell-pair relationships, like sharing a house, are 'weak' because both cells could be wrong simultaneously.
Track digit 5. We've found three 'conjugate pairs' — units where 5 fits in only two cells. Let's color the cells: A and B alternating along the chain.
Step 1 of 4 — full interactive demo available with JavaScript enabled
Ready to put your skills to the test?
Try Final Sudoku - an ad-free Sudoku experience with smart tools