Sudoku has no hidden information. Every digit you need is already determined by the clues in front of you. The only question is whether you can see it. That makes it unusual among puzzle games: there is a correct next move at every point, and "I got stuck so I guessed" always means a deduction was available and you missed it. Unless, that is, the puzzle was badly made. We'll come back to that, because we found the problem in our own.
What follows is the full ladder, cheapest technique first. That order matters as much as the techniques. Strong solvers don't hunt for clever patterns, they exhaust the boring ones first and only climb when the board goes quiet.
Rule zero: think in candidates
Every empty cell has a set of candidates: the digits not already used in its row, its column or its 3×3 box. That's the entire game. Every technique below is a rule for eliminating candidates or for noticing that only one survives.
Beginners look at a cell and ask "what goes here?" That question is usually unanswerable. The two questions that are answerable are the two singles.
1. Naked singles
A cell with exactly one candidate left. Its row, column and box between them have used the other eight digits, so only one thing fits. Write it in.
These are the easiest to spot and the easiest to run dry. On a well-made puzzle you'll get a handful at the start, then a trickle each time you place something new. Every digit you write removes a candidate from up to twenty other cells, which is why a Sudoku unlocks in cascades rather than steadily.
2. Hidden singles
The move most people never learn, and the one that does the most work. Instead of asking what fits in a cell, ask where a digit fits in a unit. Take a box and take the digit 7: if only one of its nine cells can hold a 7, then that cell is a 7, even if it has five other candidates and looks completely undecided.
This flips the search around, and it is worth drilling until it's automatic. In our own puzzles, naked and hidden singles together fill 73.5% of the empty cells on an average board before they run out. Nothing else on this list comes close. If you only ever learn one technique beyond the obvious, learn this one.
3. Locked candidates
Now the board goes quiet and you stop placing digits and start eliminating them.
Look at a box and a digit that hasn't been placed in it. If every cell that could hold that digit sits in the same row, then wherever it ends up it's in that row, so it can be cleared from that row everywhere outside the box. This is the pointing pair or triple.
It runs the other way too. If a digit's only homes within a row all sit inside a single box, it can be cleared from the rest of that box. That's claiming, or box-line reduction.
Neither one places a digit. Both shrink candidate lists, and the point of shrinking candidate lists is to manufacture singles. That's the rhythm of intermediate Sudoku: eliminate, eliminate, then collect the cascade.
4. Naked and hidden pairs
If two cells in the same unit both have exactly the candidates {3, 8}, then between them they will consume the 3 and the 8, in some order, and it doesn't matter which. Every other cell in that unit can drop both. That's a naked pair.
The hidden version is the same fact wearing a disguise, and it's much easier to walk past. If the digits 3 and 8 can only go in two cells of a unit, those two cells are the 3 and the 8, so every other candidate in them can be struck out, however crowded they looked. The pair is "hidden" because the cells are cluttered; the relationship is between the digits, not the cells.
Triples work identically with three cells and three digits, and the union is what counts: {2,5}, {5,9} and {2,9} across three cells is a valid naked triple even though no cell holds all three digits.
5. X-wing
The first technique that reasons across the board rather than inside one unit, and the last one most players ever need.
Pick a digit, say 4. Find two rows where 4 has exactly two possible cells, and those cells fall in the same two columns. You now have a rectangle. Whatever happens, one row takes its 4 in the left column and the other takes it in the right, or vice versa. Either way both columns are spoken for. So 4 can be eliminated from those two columns everywhere else on the grid. Rows and columns are interchangeable here; the pattern works in both orientations.
What we found when we audited our own puzzles
Knowing the ladder makes it measurable. So we ran all 184 scheduled dailies through a solver that uses only the techniques above, and asked which rung each one needed.
A third of them didn't answer. 32% of our daily Sudokus could not be finished by any technique through X-wing, which in practice means the player reaches a wall and has to guess and backtrack. That is a bad daily puzzle, and it was our fault: our generator removed clues while checking only that the puzzle still had exactly one solution.
That check turns out to be much weaker than it sounds. A unique solution guarantees that a computer doing exhaustive search will find the answer. It promises nothing at all about a human being able to deduce it. The two properties feel like the same thing and are not.
So we changed it. The generator now refuses to remove a clue unless the puzzle remains solvable by human technique, meaning the same ladder in this article, run after every single removal. The results after the change:
- 100% of daily puzzles are now solvable by pure deduction. None require a guess.
- 64.7% need nothing beyond singles.
- 19.6% also need locked candidates.
- 15.2% also need pairs.
- 0.5% need an X-wing.
- Nothing needs anything harder.
Two things worth noticing. First, the ladder in this article is now provably sufficient, and there is no daily you can't finish with it. Second, the puzzles got looser, not tighter: average clue count fell from 26 to about 25. Checking deducibility doesn't force you to give more away, it forces you to give away the right cells.
The fix applies to the whole Sudoku archive as well as to today's, so past puzzles are guess-free too.
When you get stuck
Work the ladder in order. Sweep for naked singles, then hidden singles, taking those by digit and unit, methodically, because that's the pass people rush. Only when both come up empty should you start eliminating: locked candidates, then pairs, then triples, then the X-wing rectangle.
And if you're properly stuck on the daily Sudoku, the deduction is definitely there. We check now.