Sudoku Techniques from Beginner to Expert
Sudoku looks like a numbers game, but it’s really a game of elimination. Every technique below answers the same question in a different way: where can this digit not go? Once you know enough “not heres,” the “must be here” answers show up on their own.
We built the grader for our Sudoku around these exact techniques, so this guide also doubles as a map of our difficulty levels. Easy and Medium puzzles need only the first two techniques. Hard puzzles need at least one from the middle of the list. Expert puzzles need an X-Wing or one of its relatives.
A quick vocabulary note: a unit is any row, column or 3x3 box. Each unit must contain 1 through 9 exactly once. A cell’s peers are the 20 other cells that share a unit with it. A candidate is a digit that could still legally go in a cell.
Naked singles
A naked single is a cell with only one candidate left. Look at an empty cell and check its row, column and box. If eight different digits already appear among its peers, the ninth digit is the answer.
Naked singles are easiest to spot in crowded areas, so check cells in rows, columns and boxes that are nearly full before anything else.
Hidden singles
A hidden single flips the question around. Instead of asking “what can go in this cell?”, ask “where can this digit go in this unit?” If a 6 is missing from a box, and every cell in that box but one is blocked, either because it’s filled or because a 6 already sits in its row or column, then that last cell is the 6. It doesn’t matter that the cell might have four other candidates.
This is the workhorse of Sudoku. The fastest way to use it is cross-hatching: pick one digit, find every copy already on the board, and mentally draw lines through their rows and columns. Then look at each box that’s missing that digit. If only one cell in the box escapes the lines, you’ve found it. Work through the digits from 1 to 9, and then start again, because every placement creates new blocks.
In our game, selecting any cell with a digit highlights every copy of that digit, which does the cross-hatching for you visually. The number pad also shows how many of each digit are left. A digit with one or two copies remaining is usually the quickest to finish.
When to start using notes
On an easy puzzle, singles alone will carry you from start to finish, and writing notes is mostly wasted effort. The moment to switch is when you’ve done a full pass over all nine digits without placing anything. At that point, the information you need is spread across several cells, and you can’t hold it all in your head.
Some habits that make notes worth it:
- Note one unit at a time. Filling candidates into all 50-plus empty cells at once is tedious and mistakes creep in. Start with the box or row that has the fewest empty cells.
- Keep notes honest. Every time you place a digit, remove it from the notes of all its peers. Our game can do this automatically. If you play on paper, make it a reflex, because an out-of-date note is worse than no note.
- Notes are for patterns. Once candidates are written, the rest of the techniques on this page become visible. Pairs, pointing pairs and X-Wings are very hard to see without them.
Naked pairs (and triples)
If two cells in the same unit have exactly the same two candidates, say {3, 8}, then those two digits are locked into those two cells. One cell will be the 3 and the other the 8, even though you don’t know which yet. Either way, no other cell in that unit can be a 3 or an 8, so you can erase those candidates from the rest of the unit.
Triples work the same way with three cells and three digits. The cells don’t each need all three digits. Candidates {1, 4}, {4, 9} and {1, 9} form a naked triple, because three cells share only three possible digits between them. Remove 1, 4 and 9 from the rest of the unit.
Naked pairs are the most common first step on a Hard puzzle. After erasing, look for new singles.
Hidden pairs
A hidden pair is a naked pair in disguise. Say that in one row, the digits 2 and 7 each appear as candidates in only the same two cells. Those two cells must hold the 2 and the 7, so any other candidates in them can be erased. A cell showing {2, 5, 7, 9} next to one showing {2, 7, 9} becomes {2, 7} and {2, 7}. Now it’s a naked pair, and you can act on it.
Hidden pairs are harder to see because the extra candidates hide them. Scan by digit: for each unit, ask “which digits appear in exactly two cells?” and then check if two of those digits share the same pair of cells.
Pointing pairs and box/line reduction
These two techniques use the way boxes overlap rows and columns.
Pointing pair. Inside a box, suppose every candidate for 5 sits in the same row. The box needs a 5, so the 5 must go in that row, somewhere inside the box. That means the rest of the row, outside this box, can’t have a 5. Erase it there. The candidates “point” along the row. The same works for columns, and for three cells in a line (a pointing triple).
Box/line reduction (also called claiming) is the mirror image. If a row’s only candidates for 5 all fall inside one box, the row’s 5 must be in that box. Erase 5 from every other cell of that box.
X-Wing
The X-Wing is the first pattern that works across two whole lines at once, and it’s the signature technique of our Expert level.
Pick a digit, say 4. Find two rows where the 4 can only go in exactly two cells, and where those cells sit in the same two columns. For example, row 2’s only spots for 4 are columns C and G, and row 7’s only spots are also columns C and G. Those four cells form the corners of a rectangle.
Row 2 must have a 4 in C or G. Row 7 must also have one in C or G. They can’t both use the same column, so one row takes C and the other takes G. Either way, columns C and G each get their 4 from rows 2 and 7. Every other cell in columns C and G can drop 4 as a candidate.
The same logic works with rows and columns swapped. The trick to spotting X-Wings is to scan one digit at a time and only look at lines where that digit has exactly two spots. If you have notes, those lines jump out.
Two relatives come up in our Expert puzzles too. The Swordfish is the same idea with three rows and three columns. The XY-Wing uses three cells with two candidates each, like {A, B}, {A, C} and {B, C}, to rule out C from any cell that sees both of the outer two.
A practical solving routine
When you sit down with a puzzle, this order works for us:
- Cross-hatch digits 1 to 9 for hidden singles. Repeat until a full pass finds nothing.
- Check crowded rows, columns and boxes for naked singles.
- Write candidates, starting with the emptiest units.
- Look for naked pairs and pointing pairs. After each elimination, go back to step 1.
- If you’re still stuck, check hidden pairs and triples.
- Scan each digit for an X-Wing.
The important part is step 4’s “go back.” Advanced techniques rarely solve a cell directly. They remove one or two candidates, and that sets off a new round of singles. Most solvers who get stuck aren’t missing a clever pattern. They’ve missed a single that a pattern just created.
Ready to try it? Start a Medium Sudoku to practice cross-hatching. When singles stop working, move up to Hard.
