Once scanning and obvious singles stop producing moves, a hard Sudoku can feel like a brick wall. It isn't — there's always a next logical step, and a handful of named techniques will get you through almost every puzzle short of expert-level. This guide walks through them in the order you should reach for them, from the everyday workhorses to the famous X-Wing.
If you're brand new, start with our how to play Sudoku guide first — this one assumes you already know the rule and use pencil marks (the candidate notes in each empty cell). Every technique below is just a way of eliminating candidates until a cell is forced.
1. Hidden singles (your bread and butter)
A hidden single is a digit that can legally go in only one cell within a row, column, or box — even if that cell shows several candidates.
Example: in a box, the digit 4 appears as a candidate in only one cell, even though that cell also lists 2 and 9. Since 4 has nowhere else to go in the box, that cell must be 4. Place it and erase the 2 and 9.
Most "hard" puzzles are really just dense with hidden singles. Train your eye to ask, for each digit in each region, "how many cells can hold this?" When the answer is one, you have a move.
2. Naked pairs
A naked pair is two cells in the same region that each contain the same two candidates and nothing else — for example two cells both showing exactly {3, 7}.
You don't know which is 3 and which is 7, but you know those two cells will consume both 3 and 7 between them. Therefore 3 and 7 can be erased from every other cell in that shared region. This often unlocks a hidden single elsewhere.
The same idea extends to naked triples (three cells sharing three candidates between them) — harder to spot, identical logic.
3. Hidden pairs
A hidden pair is the mirror image: two digits that can only appear in the same two cells within a region, even though those cells also list other candidates.
Example: in a row, digits 5 and 8 can each only go in cells A and B (no other cell in the row allows them). Then A and B must be 5 and 8 in some order — so you can erase every other candidate from A and B. Hidden pairs are easy to walk past because the clue is about where digits can't go.
4. Pointing pairs (box/line interaction)
Sometimes within a box, a digit's only candidate cells all sit in the same row or column. Example: in a box, 6 can only go in two cells, and both are in the top row of that box.
You don't know which cell is the 6 yet — but you know the box's 6 lives somewhere in that row. Therefore 6 can be eliminated from the rest of that row outside the box. This "pointing" interaction between a box and a line is one of the most useful eliminators on medium-hard puzzles.
5. The X-Wing (the famous one)
The X-Wing is the first technique that feels like magic, and it's simpler than its reputation. It works on a single digit across two rows (or two columns).
Suppose the digit 2 appears as a candidate in exactly two cells in row 4, and in exactly two cells in row 9 — and in both rows those candidates sit in the same two columns (say columns C and F). Picture the four cells as corners of a rectangle.
Here's the deduction: in each of those two rows, the 2 must go in column C or column F. Whichever way it resolves, columns C and F will each get their 2 from these rows. That means 2 can be eliminated from every other cell in columns C and F. The four corners "lock" the digit into a pattern that clears the rest of both columns.
It's called an X-Wing because the constraint crosses diagonally between the two rows and two columns.
The order to apply them
When a puzzle stalls, work down this list — easiest and most common first:
- Re-scan for hidden singles (you'll be amazed how often one appeared after your last placement).
- Look for naked pairs, then erase their candidates from the region.
- Hunt hidden pairs in any region that feels crowded.
- Check pointing pairs — does a box confine a digit to one row/column?
- Only then go looking for an X-Wing across rows and columns.
Ninety percent of the time, a move appears before you reach step 5. The discipline is in working the cheap techniques thoroughly before reaching for the exotic one.
Why bother learning the names?
Naming a pattern is what lets you see it. Before you know "naked pair," two cells reading {3,7} and {3,7} are invisible; afterward they jump off the grid. This is exactly how getting better at any puzzle works — you're building a library of recognizable shapes. We make the same argument for word games in our how to play Wordle and how to play Sudoku guides: mastery is pattern recognition, not raw effort.
Put these to work on the toughest grids you can find — and if you want a fresh supply, our best Sudoku and number puzzle games roundup has plenty. Prefer letters to digits? The same deductive muscle drives a daily round of Pairdle.