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Sudoku basics · lesson 6 of 8 · 4 minutes
When two cells reserve two digits
Understand pairs before meeting triples and quads.
Two cells, exactly two choices
Two cells in the same house both have the complete list {3, 7}. They cannot both be 3 and cannot both be 7, so one is 3 and the other is 7. We do not know their order. Together, they use both digits in that house. This is a naked pair.
For exampleIf r5c2 and r5c8 each contain only {3, 7}, remove 3 and 7 from the other cells of row 5.
The direction of removal matters
For a naked pair, remove the reserved digits from other cells in the shared house. Keep both candidates in the pair cells until something else resolves their order. Do not remove those digits from unrelated cells merely because they look nearby.
For exampleThe row pair at r5c2 and r5c8 does not by itself reserve either of their two different boxes.
A hidden pair reverses your viewpoint
Track two digits across a house. If both can occur only in the same two cells, those cells must take the two digits. Remove any extra candidates inside those cells. They may have looked crowded before you noticed the two digits had nowhere else to go.
For exampleIf 3 and 7 occur only in A {1, 3, 7} and B {3, 7, 9}, remove 1 from A and 9 from B.
Grow the idea carefully
A naked triple is three cells in one house whose combined candidates are exactly three digits. The cells need not contain identical lists. The counting is what matters. First count the cells, then the union of their digits, then identify which other cells share their house.
For example{1, 4}, {4, 8}, and {1, 8} reserve 1, 4, and 8 across three cells. Adding a candidate 6 to any one breaks that particular triple.
Quick check
Two cells in a row have lists {3, 7} and {3, 7, 9}. Is that a naked pair?
- Yes, because both mention 3 and 7.
- No, because together they still allow three digits.
- Yes, because the cells share a row.
Show the answer
No, because together they still allow three digits. Right. A naked pair needs exactly two digits across its two cells. A separate argument would have to remove 9 first.
Next, when you are ready: Naked pair.