Sudoku

Most sudoku advice online reads like a textbook nobody asked for. Here we go technique by technique, start to finish, with enough detail to actually be useful and nothing more.

If you already know the rules, skip ahead to scanning. If you don't, here's the short version.

The rules (30 seconds)

Fill every empty cell with a digit from 1 to 9. Each row, each column, and each 3x3 box must contain every digit exactly once. That's it. No math, no addition, no tricks. Just placement.

A proper sudoku has one solution. If you hit a point where you need to guess, either the puzzle is poorly made or you missed something. Usually the second one.

Scanning

This is where every solve starts, and honestly where most easy puzzles end. Scanning means looking at a number that already appears on the board and figuring out where else it can go.

Cross-hatching

Pick a number. Say it's 5. Look at each 3x3 box that doesn't have a 5 yet. For each box, check which rows and columns already contain a 5. Those rows and columns block certain cells. If only one cell remains, that's where the 5 goes.

Do this for every number, 1 through 9. Then do it again, because placing new numbers opens up new placements. Keep going until nothing new shows up.

Counting

Look at a row, column, or box that's nearly full. If 7 of 9 cells are filled, you only have two digits left to place. Sometimes one of those digits can only go in one spot based on what's already in the crossing row or column.

This feels obvious in writing. In practice, people overlook it constantly because they're focused on the empty parts of the grid instead of the full ones.

Pencil marks (candidates)

When scanning stops producing results, it's time to write down candidates. For each empty cell, note every number that could legally go there based on what's already in its row, column, and box.

Some people fill in candidates for the entire grid up front. Others do it selectively, only for areas where they're stuck. Both work. The selective approach keeps the grid cleaner; the full approach catches more patterns. Pick whichever you prefer.

On our sudoku board, you can toggle an auto-candidates mode that fills these in for you. Handy for learning, though writing them yourself builds better instincts over time.

Naked singles

After filling in candidates, some cells will have only one option. Place that number immediately and update the candidates for all cells in the same row, column, and box.

This often triggers a chain reaction. Placing one number reduces candidates elsewhere, which creates new naked singles, and so on. On easy and medium puzzles, this cascade alone can finish the grid.

Hidden singles

A hidden single is a number that appears as a candidate in only one cell within a row, column, or box. The cell might have multiple candidates, but that specific number has nowhere else to go in that unit.

Example: cell A has candidates {2, 5, 7} and no other cell in its box contains 7 as a candidate. Despite the cell having three options, 7 is the answer.

Hidden singles are easy to miss because your eye gets drawn to cells with few candidates. Train yourself to also check: for each number, where can it go in this row/column/box?

Naked pairs and triples

If two cells in the same row, column, or box have the exact same two candidates (say {3, 8}), those two numbers must go in those two cells. You don't know which goes where yet, but you can remove 3 and 8 from every other cell in that unit.

The same logic extends to triples. Three cells sharing three candidates (in any combination) lock those numbers in. It's less common and harder to spot, but the payoff is usually bigger.

The removal step is where the real progress happens. Eliminating candidates from neighboring cells often creates naked singles or hidden singles elsewhere.

Hidden pairs and triples

This is the flip side of naked pairs. Instead of finding cells with matching candidates, you find candidates that only appear in matching cells.

If the numbers 4 and 9 only appear as candidates in cells B and D within a row, then B and D must contain 4 and 9. You can remove all other candidates from B and D, potentially leaving you with a naked pair or a solved cell.

Hidden pairs require you to think about the numbers rather than the cells. It's a shift in perspective that takes practice.

Pointing pairs (box/line reduction)

Sometimes a candidate within a 3x3 box only appears in one row or one column. Since that number must go somewhere in the box, and it can only be in that row or column, you can eliminate it from the rest of that row or column outside the box.

The reverse also applies. If a candidate in a row only appears within one box, remove it from the other cells in that box. This is sometimes called box/line reduction.

Neither version changes the cells within the intersection. They only eliminate candidates elsewhere. It's a small move that often unblocks a stuck grid.

X-Wings

This is where things get interesting. An X-Wing forms when a candidate appears in exactly two cells in each of two different rows, and those cells line up in the same two columns.

Imagine the number 6 can only go in columns 2 and 7 of row 3, and also only in columns 2 and 7 of row 8. The 6 must go in one diagonal pair or the other. Either way, you can eliminate 6 from every other cell in columns 2 and 7.

It works for columns too: if a candidate is restricted to the same two rows in two columns, eliminate from the rest of those rows.

X-Wings are rare on anything below hard difficulty. When they show up, they usually break open the puzzle.

Swordfish

A swordfish is an X-Wing with three rows and three columns instead of two. If a candidate appears in at most three columns across three rows (and those are the same three columns), you can eliminate that candidate from those columns in all other rows.

Finding a swordfish by eye is genuinely difficult. Most people don't spot them without pencil marks and some deliberate column-by-column searching. If you're solving puzzles that need swordfish, you're already past the intermediate stage.

General tips

• Start with scanning. Always. Even on hard puzzles, scanning usually places a few digits before you need anything fancier.
• If you're stuck, check your pencil marks. A wrong candidate somewhere will make every advanced technique fail. Re-scan the grid from scratch.
• Focus on units (rows, columns, boxes) with fewer empty cells. They constrain faster and tend to yield placements sooner.
• Don't guess. If you find yourself thinking "maybe it's a 3?" and placing it to see what happens, you're not solving, you're gambling. Go back and look for a deduction you missed.
• Speed comes from pattern recognition, not from moving faster. Solve more puzzles at a comfortable pace and the speed follows on its own.

What each difficulty level requires

Different difficulty ratings roughly correspond to different technique requirements. Here's how our difficulty levels break down:

• Easy — Scanning and naked singles. You shouldn't need pencil marks.
• Medium — Hidden singles become necessary. Light pencil marks help.
• Hard — Naked and hidden pairs. Full candidate lists recommended.
• Expert — Pointing pairs, box/line reduction, and occasionally X-Wings.
• Einstein — Everything above, used together. Every puzzle at this level is solvable through pure logic with no guessing required. That's a guarantee.

Putting it into practice

Reading about techniques is useful. Actually applying them is where the learning happens. We'd suggest starting at a difficulty level where you can finish puzzles (even if slowly) and moving up only once that level feels routine.

Our easy sudoku puzzles use only scanning and naked singles. The hard puzzles introduce pairs. And the Einstein level is there when you want a real challenge, every puzzle certified solvable by logic alone.

If you get stuck on a specific puzzle, our hint system gives you targeted clues without spoiling the whole solution. Use it. Getting unstuck is part of learning.