How to Solve Sudoku for Beginners: A Full Puzzle, Step by Step

To solve a Sudoku as a beginner, you need just three moves. Cross-hatch one digit at a time to find the only cell left for it in a box. Scan rows and columns the same way when the boxes run dry. And when both stall, write pencil marks to find a cell with only one possible digit. Start with the digit you see most often, and never guess: a proper Sudoku has exactly one solution, so every number can be proved.

Below, those three moves solve one real Medium puzzle from start to finish, all 49 placements, each with the reason it's forced. Every step and every diagram on this page is checked by code against Poozee's Sudoku engine, so you can follow along on paper or in the game without hitting a wrong number.

Sudoku rules

• The grid has 9 rows, 9 columns and nine 3x3 boxes.
• Fill every empty cell with a digit from 1 to 9.
• Each row, each column and each box must contain every digit from 1 to 9 exactly once.
• The digits already printed (the clues) can't be changed.

That's all. There's no math: the digits are just nine different symbols. A well-made puzzle has exactly one solution, which is why logic always finds the next number and guessing is never needed. Every Poozee puzzle is checked for a unique solution when it's generated.

In the game, tap or click a cell and then a digit, or type 1 to 9. Notes (or the N key) switches the digits to pencil marks, Hint fills the selected cell, and Undo takes a move back. Tap any filled cell and every copy of that digit lights up, which makes cross-hatching much faster.

How to read the diagrams

Rows are numbered 1 to 9 from the top and columns 1 to 9 from the left, so r3c8 is row 3, column 8. Boxes are numbered 1 to 9 in reading order: box 1 is the top left, box 3 the top right, box 5 the center and box 9 the bottom right.

In the diagrams, black digits (white in dark mode) are clues, blue digits were placed in earlier steps, and the yellow cell is the step being explained. The tinted cells are the box, row or column that step looks at.

The three beginner moves

1. Cross-hatching (a hidden single in a box). Pick a digit and a box that doesn't have it yet. Every row and column that already holds that digit rules it out of the cells it crosses. If only one empty cell of the box is left, the digit goes there.

2. Scanning a row or column (a hidden single in a line). The same idea turned sideways: pick a row or column and a digit it's missing, then cross out the cells whose column, row or box already has that digit. One cell left means the digit goes there.

3. Pencil marks (a naked single). In each empty cell, write every digit its row, column and box don't already contain. A cell with only one pencil mark left has its answer. This catches cells the first two moves miss: the digit still has two or more possible spots in the cell's box, row and column, but the cell itself has room for nothing else.

Cross-hatching does almost all the work. Trying it first every time, it made 99.9% of the placements on our Easy puzzles and 97.2% on Medium (the method is in the section on levels below). The other two moves are for the moments it runs dry, and the walkthrough below has one of each.

Where to start: the digit you see most

Start with the digit that appears most often among the clues. The more copies of a digit are on the board, the more lines you can draw through each box, and the more likely one cell is left.

We measured this on 1,000 Easy and 1,000 Medium puzzles from Poozee's generator. For every digit of every puzzle, we checked whether cross-hatching could place it before anything else was filled in:

There's always somewhere to start on these levels. Right at the beginning, singles could fill 20.2 cells on an average Easy puzzle (never fewer than 9) and 12.1 on Medium (never fewer than 3). Cross-hatching boxes finds about half of them: 10.9 on Easy and 6.6 on Medium.

Pro tip: On Poozee, the small number under each digit on the keypad counts how many of that digit are still missing. The digit with the lowest count is the one to cross-hatch first.

Worked example: a Medium puzzle, step by step

This puzzle came from Poozee's generator on Medium, with 32 clues. A solver confirms it has exactly one solution. We picked it because it needs all three beginner moves at least once, so you'll see what to do when cross-hatching stops working.

Step 1: cross-hatch the 6s

Count the clues: 9 appears six times, 5 and 6 five times each. The 9s and 5s don't place anything yet (every box still missing them has at least two cells left), so move on to the 6s.

Box 3, at the top right, has no 6. Rows 2 and 3 already have one (r2c1 and r3c5), which rules out the five empty cells of box 3 in those rows. Columns 7 and 8 have one too (r6c7 and r9c8), which rules out r1c7 and r1c8. Only r1c9 is left, so it's a 6.

Steps 1 to 13: keep cross-hatching

Keep going digit by digit, box by box. Each new number is another line for the next search, so recheck the digit you just placed before moving on. "Why" names the box, then the rows and columns that rule out the rest of it.

Notice how the 8s chain together: the 8 placed in step 6 is one of the lines for step 7, and step 8's 8 helps place step 9's.

Step 14: when the boxes run dry, scan a column

After step 13, cross-hatching finds nothing anywhere: every box still missing a digit has at least two cells left for it. Time to scan rows and columns.

Column 8 has three empty cells: r1c8, r3c8 and r5c8. It has no 2 yet. Row 1 has a 2 (placed in step 3) and so does row 5 (the clue in r5c2), so the 2 can't go in r1c8 or r5c8. It goes in r3c8.

Step 15: pencil marks find a naked single

Now nothing works: no box, row or column has a digit with only one possible cell. This is the moment for pencil marks. Box 4 is a good place to try, since it has eight empty cells.

Look at r6c3. Row 6 already holds 1, 2, 3, 4, 6 and 7. Column 3 holds 2, 5 and 9. That leaves only 8. The cell had a single candidate from the start, but cross-hatching couldn't find it: the 8 for box 4 (and for row 6) could still go in r6c1 or r6c3.

Pro tip: You don't have to pencil-mark the whole grid. Start with the cells whose row, column and box are fullest: they tend to have the fewest candidates.

Steps 16 and 17: back to boxes, then a row

The new 8 gets cross-hatching going again for one step (step 16). Then the boxes run dry once more, and row 9 has the answer: its empty cells are r9c3, r9c4, r9c5 and r9c9, and the 9s in columns 3, 5 and 9 rule out all of them except r9c4.

Steps 18 to 49: cross-hatching all the way

From here on, cross-hatching never runs dry again. The grid fills up quickly, and near the end many boxes have only one empty cell left, which you can fill without any lines at all.

Out of 49 placements, 46 came from cross-hatching boxes, 2 from scanning a row or column, and 1 from pencil marks. We picked this puzzle for needing all three moves, so it stalls more than most: on a typical Medium puzzle, cross-hatching makes an even bigger share of the placements (97.2%, as measured above). The other moves are there to get you past the few spots where it stalls.

How far singles take you on each level

We solved 1,000 puzzles per level from Poozee's generator with only the three beginner moves, and checked how many each set of moves finishes on its own. "Boxes only" is cross-hatching, "boxes, rows, cols" adds row and column scans, and "pencil marks only" uses nothing but naked singles. With all three, we always tried cross-hatching first, then row and column scans, then pencil marks, as in the walkthrough:

And here is how many clues each level starts with, and how much of the grid the three moves fill before they're done or stuck:

Easy and Medium are made to be solved with these moves alone, and they always were. Hard and Expert are made to need more: none of them was solved by singles, and the three moves fill about 28% of their empty cells and then get stuck. Expert puzzles average slightly more clues than the target of 23, because the generator never removes a clue that would allow a second solution, and sometimes no clue can go.

The first table also shows why the order of the moves matters. Pencil marks alone solved only about half of the Medium puzzles, and so did cross-hatching alone, but scanning boxes, rows and columns together finished 94.5% of them without a single pencil mark.

A beginner routine for any puzzle

1. Find the digit that appears most often (on Poozee, the lowest number on the keypad).
2. Cross-hatch it in every box that's missing it, and place every 1-cell result.
3. Move to the next most common digit, and so on through all nine.
4. After every placement, recheck that digit: each new copy is another line.
5. When no box gives anything, scan each row and column for a digit with one possible cell.
6. When that fails too, write pencil marks, starting with the fullest areas, and look for a cell with one candidate.
7. Still stuck with full pencil marks? The puzzle needs the next techniques: naked pairs, pointing and X-Wing, all covered in our Sudoku strategies guide.

Keep playing

Start a Sudoku on Easy and solve it with cross-hatching alone, then try Medium and see how often you need a row scan or a pencil mark. When singles stop being enough, the Sudoku strategies guide picks up where this one ends, and the Sudoku X-Wing guide shows the first advanced pattern on real Expert puzzles. For the same kind of pure logic in a different shape, learn how to solve nonograms, or try Minesweeper with our guide on how to play Minesweeper.