Advanced foundation
Learn the candidate relationships behind many advanced Sudoku deductions.
The idea
A strong link tells us that if one is false, the other one must be true. A weak link tells us that if one is false, the others could be true.
To be more specific, a strong link tells us that if one is true, the other one must be false; if one is false, the other one must be true. A weak link tells us that if one is true, the others must be false; however, if one is false, the others might or might not be true.
The question: What does this relationship let me conclude if one candidate is true or false?
Walkthroughs
A strong link involes two cells or two numbers; a weak link involves more.
Walkthrough
Digit 6 can appear in only two cells of column 7: r4c7 and r9c7. The 6 must occupy one of those two cells. If r4c7 is not 6, then r9c7 must be 6.
What to notice: The two candidates are strongly linked because the house guarantees that at least one must be true.
Walkthrough
In column 9, the same number 6 is the candidate of three cells: r4c9, r7c9 and r9c9. if one of those three cells is not 6, it is still uncertain which of other two cells is 6.
What to notice: A weak link does not tell us that if one is false, which of others is true;
How it works
The words describe the logical relationship, not how important or powerful a candidate is. The same number can sometimes has both a strong and a weak relationship at once.
Conjugate Pair: if a number has only two possible cells in a house, one of those two cells must contain the number. If one is false, the other is forced. Those two cells form a strong link on that number.
Bivalue Cell: if a cell has only two candidates, one of those two candidates must be the solution. If one is false, the other is forced. Those two candidates have a strong link in that cell.
Inside a house: if a number appears three or more times in a house, cells containing that number form a weak link on that number, if one is false, any of others could be true.
Inside a cell: if a cell has three or more candidates, then if one candidate is false, any of others could be true. Those candidates form a weak link in that cell.
Advanced techniques connect these relationships so that a chain, pattern, or structure produces a safe candidate elimination.
A useful reminder
A strong link is not “better” than a weak link. They answer different questions. Strong links help carry a forced possibility forward; weak links tell us which possibilities cannot coexist. Together, they become the vocabulary for many later patterns. Strickly, a strong link is also a weak link, but has a special feature.
Watch & learn
Coming soon...
Next
You do not need to memorize every advanced technique at once. Start by recognizing the relationships between candidates, then see how a Fish pattern turns those relationships into a larger structural elimination.
