Sudoku Hidden Singles, Pairs and Triples: The Middle Techniques

Between "scan for obvious numbers" and "hunt for an X-Wing" sits a group of techniques that solve the large majority of hard puzzles — and hidden singles alone probably account for more missed deductions than everything else combined. These are the middle techniques: naked and hidden singles, naked and hidden pairs and triples, and pointing pairs. Learn these properly and expert-rated puzzles stop feeling impossible.

All of them require complete pencil marks. None of them work reliably without.

Naked vs. Hidden: The Distinction

This trips up almost everyone at first, so it's worth stating plainly.

Naked means you're looking at a cell and what it can be. A naked single is a cell with only one candidate left. Naked pairs are two cells that between them hold only two candidates.

Hidden means you're looking at a number and where it can go. A hidden single is a number that can only go in one cell of a unit — even if that cell shows six other candidates.

Naked patterns are easy to spot because the cell looks bare. Hidden patterns are invisible unless you deliberately go looking for them, which is exactly why they're missed.

Hidden Singles: The Most Missed Deduction

Pick a number. Pick a unit — a row, column or box. Ask: how many cells in this unit could hold that number? If the answer is one, that cell is decided, regardless of what else it lists as a candidate.

Example: a box has five empty cells. Four of them list candidates including 3; one doesn't list 3 at all. That's no help. But if only one of those five lists 3 as a candidate, then 3 goes there — even if that cell also shows 1, 4, 7 and 9.

The reason people miss these: the natural instinct is to scan cells and ask "what can this be?" That finds naked singles. Hidden singles require the opposite sweep — number first, then unit. You have to consciously choose to do it.

The practical drill: after pencil marking, take each digit 1 through 9 in turn and check all 27 units for it. It's tedious the first few times and becomes fast.

Naked Pairs

Two cells in the same unit that hold exactly the same two candidates, and nothing else.

If cells A and B in a row both show only {4, 7}, then 4 and 7 occupy those two cells in some order. Neither number can appear anywhere else in that row, so erase 4 and 7 from every other cell in it.

The pair itself doesn't get solved — that's fine. The value is in the eliminations it triggers elsewhere, which frequently create naked or hidden singles.

Important: both cells must show exactly those two candidates. If one shows {4, 7} and the other {4, 7, 9}, it isn't a naked pair.

Hidden Pairs

Two numbers that, within a unit, can only go in the same two cells.

Suppose in one box, the digits 2 and 6 each appear as candidates in only two cells, and it's the same two cells both times. Those two cells must hold 2 and 6 between them — so every other candidate in those two cells can be erased.

This is the mirror image of a naked pair: instead of cleaning up the rest of the unit, you clean up the two cells themselves.

Naked and Hidden Triples

Sudoku triples come in the same two forms as pairs — the same logic extended to three cells.

Naked triple: three cells in a unit whose candidates, combined, come to exactly three numbers. They don't each need all three — {1,4}, {4,9} and {1,9} is a valid naked triple on {1,4,9}. Those three numbers can be erased from the rest of the unit.

Hidden triple: three numbers that can only go in the same three cells within a unit. Every other candidate in those three cells can be erased.

Triples are harder to see than pairs and appear less often, but they're frequently the deduction that breaks open an expert puzzle. The partial-candidate form of the naked triple ({1,4}, {4,9}, {1,9}) is the one most solvers walk past.

Pointing Pairs and Box-Line Reduction

These two work between a box and a line, and they're the most immediately useful of the group.

Pointing pair (or triple): within one box, if a candidate appears only in cells that all sit in the same row, then that number must be somewhere in that row inside the box. So it can be erased from the rest of that row outside the box. Same logic for columns.

Box-line reduction: the reverse. If within one row a candidate appears only in cells that all sit inside the same box, then that number is in the box on that row — so erase it from the rest of the box.

A sudoku pointing pair is quick to check and produces eliminations at a good rate, and box-line reduction is no slower.

The Search Order

Work down this order, and after any placement go back to the top. If all six run dry, that's the point where advanced patterns become necessary — and where the puzzle has earned an expert or extreme rating. The full ordering, including the cheap scanning that comes first, is in sudoku strategy.

Where People Go Wrong

Marking incompletely. Every technique here reads the candidate list as truth. One missing candidate produces a false hidden single, and the puzzle breaks twenty moves later.

Not erasing after a placement. The other half of the same problem. Place a number, immediately remove it from the candidates of every cell in its row, column and box.

Only ever scanning cells. This finds naked patterns and misses every hidden one. Half your passes should be number-first.

Giving up on triples. They look intimidating written down and are much easier in practice — especially once you accept that the three cells don't each need all three candidates.

Practicing against puzzles rated hard-to-expert is the fastest way to make these automatic, since those are the puzzles that require exactly this tier and no more. Generating a run at one level with a sudoku puzzle maker drills the pattern far better than a mixed puzzle book.

Worked Examples

Reading definitions and recognizing patterns are different skills. These are the three worth walking through slowly.

Hidden single. A box has five empty cells. After marking, their candidate lists are {2,4,7}, {2,7,9}, {4,7,9}, {2,4,9} and {3,4,7}. Nothing here is a naked single — every cell has three options.

Now scan by number instead. Where can 3 go? Only one cell lists it. That cell is a 3, regardless of the 4 and 7 sitting alongside it in the list. That's a hidden single, and it's completely invisible if you only look at cells.

Naked pair. In one row, two cells both show exactly {5,8}. Between them they will use up 5 and 8. Every other cell in that row can have 5 and 8 struck out. If a third cell in the row was showing {5,8,1}, it becomes {1} — a naked single, produced entirely by the elimination.

Hidden pair. In one box, the digits 3 and 6 each appear as candidates in only two cells, and it's the same two cells. Those two cells must hold 3 and 6 between them, so every other candidate in those two cells is struck out. A cell showing {1,3,4,6,7} becomes {3,6}.

Notice the symmetry: a naked pair cleans the rest of the unit; a hidden pair cleans the two cells themselves.

Spotting Them Faster

For hidden singles, scan by digit and unit systematically. Digit 1 across all nine rows, then all nine columns, then all nine boxes. Then digit 2. It feels mechanical and it's the only reliable way — hidden singles do not announce themselves.

For naked pairs, look for short candidate lists. Any cell showing exactly two candidates is a pair candidate. Scan its row, column and box for a matching pair. Cells with two candidates are visually distinctive once you're looking for them.

For hidden pairs, count candidate frequency per unit. Within one box, tally how many cells list each digit. Any digit appearing in exactly two cells is a hidden-pair candidate; check whether another digit appears in the same two.

For pointing pairs, work box by box. For each box and each candidate digit, ask whether all its possible cells share a row or a column. If so, eliminate along that line outside the box.

Why These Techniques Get Missed

Hidden patterns require a deliberate change of direction. After pencil-marking, everyone's instinct is to read cells. Hidden singles, pairs and triples all require reading digits instead. Nothing prompts that switch, so it has to be a conscious habit.

Triples look harder than they are. Written out, "three cells whose combined candidates total exactly three digits" sounds abstract. In practice you're looking at three short lists and checking whether their union has three members. The partial form — {1,4}, {4,9}, {1,9} — is the one people walk past, because no single cell contains all three digits.

Eliminations feel less satisfying than placements. A naked pair doesn't fill a cell; it just removes candidates. Solvers chasing the satisfaction of writing a number in undervalue the eliminations that make the next placement possible.

Marks go stale. Every technique here reads the candidate lists as truth. If a placement three moves ago wasn't propagated, the pattern you find will be false — and you won't discover it until the grid contradicts itself much later.

Where Each Technique Pays Off Most

Not all four are equally useful at every stage of a solve, and knowing when to reach for which saves real time.

Early solve, marks just completed. Naked singles first — a fresh marking pass usually leaves several cells with one candidate. Then a full hidden-single sweep, which at this stage tends to produce the most placements per minute of any technique.

Mid solve, placements slowing. Naked pairs and pointing pairs. These rarely place a number directly but they strip candidates, and the eliminations frequently create singles a pass later.

Late solve, few cells left. Hidden pairs and triples. With most of the grid filled, candidate lists are short and the patterns become much easier to see. A triple that was invisible twenty moves ago can be obvious now.

Stuck completely. Re-verify the marks before assuming you need an advanced technique. A substantial share of apparent dead ends are actually a stale candidate somewhere.

Keeping Candidate Marks Reliable

Every technique here reads the pencil marks as truth, so the marks are the foundation everything rests on.

Propagate immediately. The instant you write a number in a cell, strike it from every candidate list in that row, that column and that box. Not after the next deduction — immediately, before doing anything else.

Mark in a consistent position. Writing candidates in fixed positions within the cell — 1 top-left, 2 top-center, and so on — lets you read a cell at a glance rather than parsing a jumble. It also makes a missing candidate visible as a gap.

Do a verification pass at the halfway point. Pick one box and re-derive its candidates from scratch. If it matches what you have, the rest is probably sound. If it doesn't, redo everything.

If you find one error, redo them all. An error usually means a systematic slip rather than a one-off, and patching a single cell leaves the others wrong.

Building Recognition Speed

These techniques are pattern recognition, and pattern recognition responds to volume rather than study.

Drill one technique at a time. Solve four or five puzzles hunting deliberately for hidden singles and nothing else, even when a naked pair is sitting there. Isolating the search teaches your eye what to look for far faster than mixed practice.

Say what you're doing out loud. "Where can 4 go in this box?" Naming the search keeps you in number-first mode rather than drifting back to scanning cells.

Work at one difficulty until it's comfortable. Hard-rated puzzles are the right level for this tier — they require these techniques and rarely require anything beyond them, which makes them concentrated practice.

Expect the shift to be sudden. Most solvers describe hidden singles going from invisible to obvious over a week or so rather than gradually. Before the shift, the sweep feels mechanical; afterwards you spot them while scanning for something else.

Locked Candidates: The Name That Covers Pointing and Claiming

Pointing pairs and box-line reduction have a shared umbrella name that causes real confusion when you move between books, apps, and solvers: locked candidates. The candidate is "locked" into an intersection between a box and a line, and which direction the elimination runs depends on which unit does the locking.

Locked candidates type 1 — pointing. All remaining copies of a digit inside one box sit in a single row or column. The digit is therefore in that box somewhere along that line, so it can be erased from the rest of the line outside the box.

Locked candidates type 2 — claiming, sometimes called line-box reduction. All remaining copies of a digit inside one row or column sit inside a single box. The digit must land in that overlap, so it can be erased from the rest of the box.

Same geometry, opposite direction. The intersection of a box and a line is three cells, and whichever unit confines the digit to those three cells removes it from everywhere else in the other unit.

The naming matters mainly because step-by-step solvers announce these deductions by name and rarely explain them. When a tool says "locked candidates in box 5," it is describing exactly the technique in the section above — check which unit was doing the confining before you start erasing, since applying the elimination in the wrong direction produces a wrong candidate list and an unrecoverable grid.

What "Intermediate Sudoku" Actually Means

Difficulty labels vary between publishers, but the intermediate tier has a reasonably consistent technical definition: a puzzle that cannot be finished by scanning and singles alone, but never requires anything beyond the techniques on this page.

In practice that means an intermediate puzzle will stall once or twice. Basic scanning gets you fifteen or twenty placements, then stops. Pencil marks go in, naked and hidden singles clear a few more cells, and then a pair or a pointing set is the only thing standing between you and a cascade of easy placements. Find it, and the rest of the grid usually falls in a few minutes.

That stall-and-unlock rhythm is the signature of the tier, and recognizing it is useful — it tells you the deduction you need is on this page rather than in the advanced techniques, so there is no reason to start hunting for an X-Wing.

A reasonable self-test for whether you have moved past intermediate: can you finish a puzzle rated hard by most sources without any deduction beyond pairs, triples, and locked candidates? If yes, you are ready for expert grids, where those techniques run out and single-digit patterns across multiple lines become necessary. If puzzles at this level still stall permanently, the gap is almost always hidden singles or unreliable candidate marks rather than a missing advanced technique.

Frequently Asked Questions

What's the difference between a hidden single and a naked single? A naked single is a cell with only one candidate remaining. A hidden single is a number that can only go in one cell within a row, column or box — even though that cell may still list several other candidates.

Why do I keep missing hidden singles? Because finding them requires scanning number-first ("where can this 3 go in this box?") rather than cell-first ("what can this cell be?"). Most solvers default to cell-first scanning, which only reveals naked patterns.

Do naked pairs have to be in the same box? No — they must be in the same unit, which means the same row, the same column, or the same box. Any one of the three works, and the eliminations apply to that unit.

How often do triples actually come up? Less often than pairs, but regularly enough in expert-rated puzzles to matter. They're frequently the single deduction standing between a stuck grid and a solved one, which is why they're worth learning despite being rarer.

Do the three cells in a naked triple all have to show all three candidates? No, and this is the most common reason triples get missed. The three cells must collectively contain only three distinct candidates between them — so {1,2}, {2,3}, {1,3} is a valid naked triple even though no cell holds all three.

What is a pointing pair in sudoku? A digit whose only remaining cells within a box all sit in the same row or column. Because the digit must go somewhere in that box, it must fall on that line inside the box, which lets you erase it from the rest of that row or column outside the box.

What is the locked candidate sudoku technique? It is the umbrella name for pointing and claiming. A digit confined to the three cells where a box and a line overlap has to land somewhere in that overlap, so it can be erased from the rest of whichever unit did not do the confining.

Are pointing pairs and locked candidates the same thing? Pointing is one of the two locked candidate types. Pointing runs box-to-line; claiming runs line-to-box. Solvers and apps often report both simply as "locked candidates," so check which unit confined the digit before applying the elimination.