Naked Pairs, Triples and Quads Explained

If two cells in the same row, column, or box have exactly the same two candidates and nothing else, those two digits must go in those two cells. That means you can erase both digits from every other cell in that unit. This is a naked pair, and it's usually the first technique you need once singles run out.

Triples and quads are the same idea with more cells: three cells that together hold only three digits, or four cells holding only four. This technique needs notes. If you're not writing candidates yet, start with naked and hidden singles.

Naked pairs: the logic

Say two cells in a row both have candidates {3, 7} and nothing else. One of them is a 3 and the other is a 7. You don't know which is which yet, but it doesn't matter: the 3 and the 7 for that row are spoken for. No other cell in the row can be a 3 or a 7.

Erase those 3s and 7s from the rest of the row. Often one of those cells is left with a single candidate, and you're back to placing singles. If the two cells also share a box, check the box too: the pair clears candidates from both units.

Naked triples: the part people get wrong

A naked triple is three cells in one unit whose candidates, combined, are only three digits. Each cell does not need all three. For example:

• Cell A: {2, 5}
• Cell B: {5, 8}
• Cell C: {2, 8}

Together they contain only 2, 5 and 8, and there are three cells, so those three digits must fill those three cells. Remove 2, 5 and 8 from every other cell in the unit. This is why triples are easy to miss: you're looking for three cells that look different from each other but share a small pool of digits.

Quads

Four cells, four digits, same rule. Quads are rare and hard to see. In practice you'll usually find the matching hidden subset first: if a unit has a naked quad, its remaining empty cells form a hidden subset, which is often easier to spot. See the Hidden Pairs lesson.

How to find them fast

1. Scan for cells with exactly two candidates. These are the only possible members of a naked pair.
2. Look for a twin in the same unit. Check that cell's row, column and box for another cell with the identical pair.
3. For triples, look at crowded units. A row with four or five empty cells is the most likely place for a triple.
4. After every elimination, check for singles. A pair's main job is to unlock the next single.

Common mistakes

• Pairs across different units. Two {4, 9} cells only form a pair if they share a row, column or box.
• Stale notes. A candidate you forgot to erase can create a fake pair or hide a real one.
• Removing digits from the pair itself. The eliminations apply to the other cells in the unit, never the pair's own cells.

Practice

Finish with Subsets: Mixed Practice, which mixes pairs, triples and hidden pairs. Then play a Hard puzzle with notes on and see how many pairs you can find.