All of sudoku's logic rests on four pillars. Without them, tougher puzzles stay unsolved; master them, and most become manageable. But there's a gap between knowing a technique and seeing it on the grid — and what bridges that gap is visual practice.
Each technique is covered here in three layers: first what it is, then how it works, and finally how it looks in a real grid example. The order isn't arbitrary — without elimination, naked singles stay invisible; without naked singles, naked pairs are useless; and pointing pairs assume both.
- Elimination: Which digit can't go in this cell?
- Naked Single: Finding the cell that can only hold one digit
- Naked Pair: Using two cells that share exactly the same two candidates
- Pointing Pairs: Converting a box's candidate distribution into a row or column cleanup
Elimination
Elimination is the foundation of all sudoku logic. Every other technique — including naked singles — builds on top of it. The central question is: "Can this digit go in this cell?" The answer comes down to three rules.
Three Rules, One Logic
The sudoku rule is simple: every row, every column, and every 3×3 box contains the digits 1 through 9 exactly once. Elimination works by reversing that rule: if a digit is already present in a row, column, or box, it can't appear in any other cell of that same row, column, or box.
Visual Example — Elimination
Step-by-Step Solution
The 4 goes in this cell. There's no other option. Not a guess — a deduction.
You need to run elimination mentally not just on empty cells, but on filled ones too. The question "does this 7 here affect that cell?" should be asked for every digit already on the board. This habit starts running automatically before you even begin looking for naked singles.
Naked Single
If only one digit can go in a cell, that digit must go there. It's called "naked" because the cell sits right out in the open with its single candidate — not hidden, just proven.
Finding a naked single requires a candidate list: the set of all digits that can still go in a cell after elimination. The moment that list hits one entry, a naked single has appeared.
How to Build the Candidate List
For each empty cell, ask: which digits from 1 to 9 can't go here? Cross off every digit already present in the same row, column, or box. What's left is that cell's candidate list.
On Sudokum.Net, the N key activates note mode. Digits entered in note mode are saved as small candidate annotations inside the cell. This lets you spot naked singles visually on the grid rather than tracking them in your head.
Visual Example — Naked Single
Step-by-Step Solution
You don't need to scan every cell in the grid to find a naked single. The efficient approach: start with rows and columns that already have the most digits filled in. If a row has 7 or 8 digits, one or more of its empty cells is likely a naked single.
A naked single is cell-based — "only one digit fits here." A hidden single is digit-based — "this digit, in this row, can only go here." Both identify a single candidate, but from opposite directions. Naked singles are found through the candidate list; hidden singles, by analyzing the digit's distribution.
Naked Pair
Naked pairs require a slightly more advanced way of thinking. The idea: if two cells share exactly the same two candidates and belong to the same row, column, or box, those two candidates can be eliminated from every other cell in that unit.
Why? Because those two digits will definitely end up in those two cells — even if we don't yet know which goes where. That certainty makes keeping those two digits as candidates elsewhere in the unit pointless.
Visual Example — Naked Pair
Step-by-Step Solution
Second Example — Naked Pair Inside a Box
It's slow at first — you have to compare candidate lists cell by cell. In experienced solvers, that comparison is automatic: when they spot a cell with two candidates, they reflexively check whether a matching cell exists. That reflex typically clicks in after 50 to 100 puzzles.
Pointing Pairs
Pointing pairs are an observation about how candidates are distributed inside a box. If a digit's candidates within a single 3×3 box all fall on just one row or one column, that digit can be eliminated from the cells of that row or column that lie outside the box.
That's where the name comes from: those two (or three) cells are "pointing" outward along the row or column. It's the only technique that takes a conclusion from inside a box and carries it into the row or column dimension.
Visual Example — Pointing Pairs Along a Row
Step-by-Step Solution
Second Example — Pointing Pairs Along a Column
Pointing pairs work from the box outward to the row or column. Box/line reduction is the reverse — it spots that a candidate in a row or column is confined to a single box and clears the rest of that box. Two complementary directions, the same underlying logic.
What Order to Apply the Techniques?
Order matters — skipping a technique can make the next one invisible. An efficient solving routine works like this:
| # | Technique | When? |
|---|---|---|
| 1 | Elimination | Build or update the candidate list for every empty cell. |
| 2 | Naked Single | Any cells with a candidate list down to one digit? Fill them in. |
| 3 | Hidden Single | Scan each digit across every row, column, and box. If it fits in only one cell, write it in. |
| 4 | Naked Pair | Any pairs of cells sharing the same two candidates? Apply the effect. |
| 5 | Pointing Pairs | In each box, are any digit's candidates confined to one row or column? If so, clean outward. |
When you're stuck, go back to the top of this sequence. Every time a technique produces progress, you need to restart from step one — because changing one cell affects the candidate lists of others.
The Game Coach's Teaching mode shows in real time which technique can be applied. Instead of keeping the sequence above in your head, the Game Coach analyzes the current grid state and suggests the right technique. Invaluable during the learning phase — but don't read the hint before you've tried to spot the technique yourself.
Frequently Asked Questions
To Wrap Up
The gap between knowing these four techniques and seeing them on the grid closes with practice. You were already doing elimination — just not systematically. Once you start spotting naked singles, the grid looks different; with naked pairs, you feel the logic of the chain. Pointing pairs show you how a box "talks" to its row and column — and at that moment, the way you see puzzles changes.
Make elimination a habit — without candidate notes the naked pair stays hidden, and without the naked pair the pointing pairs are useless. Each technique builds on the one before it — which is why the order isn't optional.