The Sudoku Technique Ladder: Naked Singles to X-Wing
There are 6,670,903,752,021,072,936,960 ways to fill a sudoku grid — Bertram Felgenhauer and Frazer Jarvis counted them in 2005. Your puzzle points at exactly one, and a properly made puzzle lets you walk there step by step without guessing once. What separates people who finish hard grids from people who stall isn't talent or eyesight. It's knowing the techniques in the right order, so you always reach for the cheapest tool that still works.
Here's the ladder, bottom rung first. Climb only as high as the puzzle forces you.
Step zero: scan on a system
Random staring finds random things; a routine finds everything, in order:
- Count each digit's appearances first. A digit already placed seven or eight times is nearly done, and its last cells often place themselves.
- Take one digit at a time and sweep the boxes. Which boxes lack it, and which rows and columns already carry it? This cross-hatching produces most of the easy placements.
- After every placement, look locally. A new digit changes its own row, column and box, so the next move usually sits within arm's reach of the last one.
The routine matters more on hard puzzles, not less. Advanced patterns only become visible after the basics have squeezed the grid, so a sloppy scan hides exactly the structures you'll be hunting later.
Rung one: singles
Naked singles
A cell whose row, column and box already rule out eight digits has one candidate left, so write it in. Easy grids are nearly all naked singles; on Inkplay's sudoku, the easy setting rarely demands anything beyond this rung and the next, which makes it the right place to build the scanning habit until it runs without thought.
Hidden singles
Now flip the question: not what fits in this cell, but where a digit can still live inside one unit. If the 4 has a single legal cell left in a box — even a cell that carries five other candidates — the 4 goes there, and those other candidates were noise. Hidden singles hide because the cell looks busy. The digit doesn't care how busy the cell looks.
Rung two: pairs, naked and hidden
Two cells in one unit that both hold exactly 3 and 7 lock those digits between them — one takes the 3, the other the 7, whichever way around. Every other cell in that unit can drop both candidates. That's a naked pair, and notice it places nothing. It only deletes, and the deletions are the point, because they cascade into fresh singles your scan will now catch.
The hidden pair is the mirror image. If 3 and 7 can only appear in the same two cells of a unit, those cells are spoken for, and every other candidate written in them can go. Hidden pairs are genuinely hard to see in a forest of pencil marks, which is why marks earn their keep from this rung upward — kept lazily, they're worse than none.
Rung three: pointing pairs and box-line reduction
These are the first moves that reach across units. Inside a box, if every remaining spot for a digit sits on one row, then wherever it lands, that digit occupies that row inside that box — so erase it from the same row's cells in the other two boxes. That's a pointing pair, or a pointing triple. Box-line reduction runs the identical logic backwards: when a row's only spots for a digit all fall inside one box, clear that digit from the rest of the box. Neither move writes a number. Both quietly demolish the middle of a hard puzzle, and medium-to-hard grids lean on them constantly. If singles have dried up, this is nearly always where the next thread is.
Rung four: the X-wing, and why you never guess
Take one digit — say 7 — and find a row where it's restricted to exactly two columns. Now find a second row restricted to the same two columns. Those four cells form a rectangle, and the two 7s must sit on one diagonal or the other; either way, both columns receive their 7 from those two rows. So every other 7 candidate in those columns is wrong. Erase them all. The X-wing is where sudoku starts feeling like structure rather than bookkeeping, and it's as high as the ladder needs to go for nearly anything published as hard.
Which raises the question of guessing. A proper sudoku has exactly one solution, and every clue participates in forcing it. A grid with two solutions can't be finished by logic at all, only gambled on, since no constraint distinguishes the twins — and that's a construction flaw, not a difficulty level. Our generator solves each candidate puzzle internally and verifies the solution is unique before serving it, so on an Inkplay grid, being stuck carries a useful message: some cheaper rung still holds a move you haven't found. Go back down the ladder before you reach up. Bifurcating — penciling in a guess and playing forward — also costs more than it looks, since one wrong branch discovered twenty placements later means unwinding all twenty.
When the ladder feels automatic, it transfers almost unchanged. Word sudoku swaps digits for letters and changes nothing else — a hidden single feels strange when the candidates spell something, but it's the same move. Kakuro welds the no-repeat rule to arithmetic, suguru trades the boxes for irregular cages plus a rule that touching cells never match, and the click-by-click deductions of minesweeper run on the same refusal to act without proof.