How to Solve Sudoku: A Step-by-Step Method

To solve a sudoku, you repeat one loop: look for the easiest move on the board, make it, and look again. The easiest moves are singles, which place a digit directly. When there are none left, you write in candidates and use elimination techniques until a single appears. Guessing is never required. This guide walks through that loop, step by step, and explains what to do at each difficulty level and when you get stuck.

If you have never played before, read the rules of sudoku first. The short version: every row, column, and 3x3 box must contain the digits 1 to 9 exactly once.

Step 1: scan for full houses

Look for any row, column, or box with only one empty cell. Fill in the missing digit. This is a full house, and it takes no thought at all. Fresh puzzles rarely have one, but the end of every solve is full of them.

Step 2: scan digit by digit for hidden singles

Pick a digit that already appears many times, say 7. For each box that does not have a 7 yet, look at the rows and columns that already contain a 7 and rule out those lines inside the box. If only one empty cell in the box survives, the 7 goes there. This is called cross-hatching, and each placement it finds is a hidden single.

Go through the digits from most common to least common. On an easy puzzle, this step alone places most of the digits.

Step 3: check crowded cells for naked singles

Find empty cells where a busy row meets a busy column. List the digits the cell's row, column, and box already contain. If eight different digits are present, the ninth goes in. That is a naked single.

Step 4: follow the cascade

Every digit you place changes one row, one column, and one box. Check those three groups right away: the placement often creates a new full house or single nearby. Following these chains is faster than rescanning the whole grid, and it is the single biggest habit that separates quick solvers from slow ones.

On easy puzzles, steps 1 to 4 finish the job. Keep looping until the grid is full.

Step 5: write in candidates

When a full scan finds nothing, you are on a medium or harder puzzle. Write the possible digits in small print in each empty cell. These are pencil marks (called notes in most apps). Two styles work:

• Full marks: every possible digit in every empty cell. Slow to fill, but you will need them for pairs and anything harder.
• Snyder marks: only mark a digit in a box when it has exactly two possible cells there. Faster, and enough for most medium puzzles.

Notes are where harder puzzles are won. Among Sudoku Royale players, notes are used on under a fifth of Easy puzzles and on more than four out of five Expert ones.

Step 6: eliminate candidates

Now use techniques that remove candidates. Try them in this order, and go back to step 1 as soon as any of them produces a single:

1. Pointing and claiming: a digit locked to one line inside a box, or to one box inside a line.
2. Naked pairs and hidden pairs.
3. Naked triples and hidden triples.
4. X-Wing, Swordfish, XY-Wing, and simple coloring for hard and expert puzzles.

The order matters. Always use the cheapest technique available. An expert puzzle might need one X-Wing and fifty singles. Looking for the X-Wing first wastes time. The full list, with what each technique does, is in our sudoku techniques guide.

What to do when you are stuck

• Recheck your notes. A missed candidate removal is the most common reason a solve stalls. Look for a digit sitting in the notes of a cell that already sees it.
• Count each digit. Write down how many of each digit are placed. The ones at seven or eight have only one or two spots left, which makes them easy to finish.
• Scan by group, not by cell. Pick the box or row with the fewest empty cells and ask, for each missing digit, where it can go.
• Take a nudge, not the answer. A good hint tells you which technique to look for and lets you find the move yourself. In Sudoku Royale's Practice mode, a hint bulb lights up after 90 seconds without a correct placement (you can tap it sooner). It names a technique that works on the board right now, with a one-line reminder of how it works and a button to open the lesson. For singles, it also highlights the cell, but you still work out the digit. See how sudoku hints work.
• Work down a checklist. Our stuck checklist puts the techniques in the order to try them, with a worked example grid for each step.

How to solve by difficulty

• Easy: steps 1 to 4 only. No notes needed.
• Medium: singles plus Snyder marks, pointing, and the odd naked pair.
• Hard: full notes, pairs and triples, sometimes an X-Wing.
• Expert: full notes and at least one advanced pattern.

More detail on what each level asks of you is in sudoku difficulty levels explained. When the method feels natural and you want to cut your times, move on to how to solve sudoku faster.