Naked Pairs, Hidden Pairs & Triples
The intermediate techniques that carry you through most hard puzzles
Once scanning and singles stop being enough, pairs are the next weapon — and for most players they're the technique that unlocks the biggest jump in difficulty. The idea behind every version is the same: when a small set of digits is locked into a small set of cells, everything else can be swept away.
Naked pairs
A naked pair is two cells in the same row, column, or box whose pencil marks show exactly the same two candidates — and nothing else. Say two cells in a row both read "3, 7":
One of those two cells must be the 3 and the other must be the 7 — there's no third option in either cell. You don't yet know which is which, and you don't need to. Between them they use up the 3 and the 7 for that row, so you can erase 3 and 7 from every other cell in it. The cell showing [1379] becomes [19]; the [379] becomes [9] — a solved cell, from nothing but bookkeeping.
Why it works
Two cells, two candidates, no alternatives. If a 3 appeared anywhere else in the row, both pair cells would have to be 7 — two 7s in one row, which is illegal. The pigeonholes are full.
Hidden pairs
The hidden pair is the same logic viewed from the other side, and it's the one solvers miss most often. Here, two digits appear as candidates in only two cells of a group — but those cells are cluttered with other candidates that camouflage the pattern.
The 2 and the 8 must live in those two cells — nowhere else in the box can host them. That means those cells can contain nothing but the 2 and 8: strip the other candidates, and the clutter [2489] and [1258] collapses to a clean naked pair [28] [28]. Often the eliminations that follow crack the whole region open.
How to actually spot hidden pairs
- Count digit appearances per group. For each digit, ask: how many cells in this box (or row, or column) could still hold it? Any digit with exactly two homes is a pair candidate.
- Look for a second digit sharing the same two homes. Two digits, same two cells — that's the hidden pair.
- Work boxes first. Nine cells are easier to audit than a full row scattered across the grid.
Triples: the same idea, one size up
A naked triple is three cells in one group that between them hold only three distinct candidates — for example [16], [68], and [18]. No single cell needs all three digits; what matters is that the trio's combined options are just {1, 6, 8}. Those three digits are locked into those three cells, so they can be erased from the rest of the group.
Hidden triples mirror hidden pairs: three digits confined to three cells, buried under other candidates. They're rarer and harder to see, but the counting method above finds them the same way — you're just looking for digits with two or three possible homes that overlap.
A 30-second drill for every stuck moment
- Pick the most crowded box on the grid.
- For digits 1–9, count possible homes in that box.
- Two digits with the same two homes? Hidden pair — clean the two cells.
- Two cells with identical two-candidate marks? Naked pair — clean the rest of the group.
- Re-scan for new singles and repeat.
Pairs show up constantly from the mid-game onward in Cosmic Sudoku's difficulty curve — roughly from the lunar levels on. If you can find them without prompting, you're ready for the X-Wing and Swordfish. And if this page felt fast, start with the fundamentals in how to play and the broader strategy guide.