How Sudoku Puzzles Are Made (and Why Each Has One Solution)

Every Sudoku you solve was once a finished grid. Somebody, or something, filled in all 81 cells and then carefully took most of them away, leaving just enough clues for you to find your way back. But how do they decide which digits to keep? Why does a good puzzle always have exactly one answer? And can a computer make a puzzle as well as a person? Here is a behind-the-scenes look at how Sudoku puzzles are made, including exactly how we make the ones on Sudoku.my.

How are Sudoku puzzles made? The short answer

The basic recipe: fill, then remove

It can seem as if a puzzle setter starts with a few clues and hopes they work out. In practice it nearly always runs the other way round: you start with the answer and work backwards to the puzzle. Think of a sculptor with a block of stone. The finished statue is already inside it; the work is in knowing what to chip away.

It’s easiest to see on a small 4×4 Sudoku, where each row, column and 2×2 box needs the digits 1 to 4. Here is a complete grid, followed by the puzzle that was carved out of it.

This puzzle was made by a small program that removed the cells in a random order. Each time, it checked two things: that the puzzle still had only one solution, and that it could still be solved with simple moves. If either check failed, the digit went back in. A 9×9 puzzle is made in exactly the same way, just with far more cells to test.

Step 1: building a complete grid

You can’t just scatter digits across a grid and hope. Each new digit has to fit its row, its column and its box, and an early choice can quietly make the grid impossible to finish twenty cells later. So most generators use a method called backtracking:

1. Pick an empty cell.
2. Try a digit that doesn’t clash with anything in the same row, column or box.
3. Move on to the next empty cell and repeat.
4. If you reach a cell where no digit fits, step back to the previous cell, try its next option, and carry on from there.

It is a brute-force search, but a quick one, especially with a common shortcut: always fill the cell with the fewest possible options first, so dead ends show up early. To get a different grid every time, the program tries the digits in a shuffled order. With roughly 6.67 sextillion valid 9×9 grids to land on (our post on how many Sudoku puzzles there are explains that number), a generator is never going to run out.

Step 2: taking clues away

Now the setter has 81 digits and wants perhaps 25 to 40 of them. The usual approach is to remove the digits one at a time, in a random order, and test the puzzle after each removal:

• Still exactly one solution? Keep the cell empty and move on.
• Now two or more solutions? Put the digit back. This clue is needed.

If you keep going until no single clue can be removed without allowing a second answer, you have what mathematicians call a minimal puzzle: every remaining clue is doing a job. Most puzzles in newspapers and apps are not minimal, because the setter stops early to hit a target number of clues or a particular difficulty.

There is a limit to how far you can go. In 2012, Gary McGuire, Bastian Tugemann and Gilles Civario showed with an exhaustive computer search that no 9×9 Sudoku with only 16 clues has a unique solution, so 17 clues is the minimum. Most generators never get near it; a random grid usually stops being carvable well before that.

Why every puzzle needs one solution

A properly made Sudoku has exactly one solution. That is what makes it fair. If two grids both fit the clues, then somewhere there are cells where no amount of reasoning can tell you which digit belongs. You would have to guess, and you might finish a perfectly valid grid and still be told you were wrong because the setter had the other answer in mind.

A unique solution is also a quiet promise from the setter to you: every cell can be worked out, one deduction at a time. That promise is why, when you are stuck, the right response is to look harder rather than to guess. (If that’s where you are right now, our guide to what to do when you’re stuck may help.)

There are two common ways to check uniqueness while a puzzle is being made:

The second method is stricter. Each logical step only places a digit that must go there, so if the steps fill the whole grid, there was never room for a second answer.

Grading difficulty by human techniques

Once a puzzle has one solution, the next question is how hard it is. It is tempting to count the clues, but that turns out to be a weak guide. What matters much more is the hardest technique a person needs to solve it.

So setters, and the programs they use, solve each puzzle the way a careful human would: always looking for the simplest move first, and only reaching for a harder technique when nothing simpler works. The trickiest move needed along the way decides the grade. A puzzle that falls to hidden singles is easy; one that needs an X-Wing is not, however many clues it starts with.

We won’t repeat the whole ladder of techniques here. Our guide to Sudoku difficulty levels shows what each level asks of you, with a real move from each one.

Symmetry: why the clues make a pattern

Look at the starting clues of a printed Sudoku and you’ll often notice they form a pattern. Turn the page upside down and the clue positions look the same. That is rotational symmetry: if the cell in row 1, column 2 has a clue, so does the cell in row 9, column 8.

Symmetry has nothing to do with solving. The digits in mirrored cells are usually different, and a symmetrical puzzle is no easier or harder than any other. It is purely about looks and craft. The Japanese publisher Nikoli, which gave Sudoku its name, says that in 1986 it decided on a rule for making the puzzle: the clues must be arranged in a symmetrical pattern. Many newspapers and books have followed that tradition ever since.

Hand-made puzzles: the Nikoli tradition

Not every Sudoku comes from a computer. Nikoli, the company whose magazine introduced the puzzle in Japan in 1984 (our history of Sudoku tells that story), is known for making its puzzles by hand, and explains why on its website.

A human setter works differently from a generator. Instead of starting from a full grid, they often place clues with a solving path in mind: an easy opening, a satisfying middle, a key moment where one clever deduction unlocks the rest. They solve as they build, adjusting clues until the path flows and the answer is unique. Nikoli’s chief editor, Nobuhiko Kanamoto, argues that computer puzzles often lack this sense of flow, and sums up the goal like this: “The best Sudoku make you concentrate, but aren’t stressful.”

Computers arrived early, too. The puzzles that launched the craze in The Times in 2004 came from Wayne Gould, a New Zealander and retired judge in Hong Kong, who had spent about six years writing a program to produce puzzles and rate their difficulty. Today most puzzles you meet in apps and newspapers are made by software, while hand-made puzzles remain popular with enthusiasts.

Neither is automatically better. A careless generator can make dull or unfair puzzles, and a careful one can make excellent ones. What matters is what the program, or the person, checks for.

Why some puzzles seem to need guessing

If you’ve played Sudoku in a few different apps, you may have met a puzzle where you were sure you had tried everything, and the only way forward seemed to be trial and error. There are a few possible reasons:

• The generator only checked uniqueness. A brute-force solver can confirm that a puzzle has one answer even when a human needs a very advanced technique, or a lot of trial and error, to find it. If nobody checks that the puzzle can be solved with known logical techniques, some of these slip through.
• The grading stops too early. A rating may only look at the start of the puzzle, or simply count clues, so a puzzle labelled “Medium” can hide one very hard step in the middle.
• The puzzle really is extreme. Some puzzles are deliberately built for experts and need techniques far beyond the usual ones. Solvers who enjoy them would call it logic, not guessing, but it can feel like guessing if you don’t know the technique.
• A mistake earlier on. Sometimes the puzzle is fine and a wrong digit or a missing pencil mark has blocked the path. Our list of common Sudoku mistakes covers the usual culprits.

The fix on the setter’s side is simple to describe: don’t just ask “is there one answer?” but also “can a person reach it with these techniques?” That is the approach we take.

How Sudoku.my makes its puzzles

Here is what actually happens when Sudoku.my makes a puzzle, in plain language. Every level is made by the same generator; only its settings change.

1. Build a complete grid. A backtracking search fills an empty grid, always choosing the cell with the fewest options and trying digits in a shuffled order.
2. Pick a target. Each level has a range of clues to aim for. The generator picks a number at random within that range.
3. Remove clues in symmetric pairs. It goes through the cells in a random order and removes each one together with its mirror image (the cell you get by turning the grid upside down), like printed puzzles.
4. Check with a human-style solver. After every removal, a solver that only uses techniques a person can follow tries to finish the puzzle, using only the techniques allowed for that level. If it can’t, the digits go back.
5. Remove single cells. When no more pairs can go, it tries removing single cells the same way, until it reaches the target. Most puzzles end up largely symmetrical, but not always perfectly so.
6. Make sure the level is earned. The harder levels must actually need harder techniques. If the finished puzzle turns out too easy, the generator starts again with a fresh grid, trying up to 40 grids and keeping the best one it finds.

Because the checking solver never guesses, it does two jobs at once. When it fills the whole grid, that proves the puzzle has exactly one solution, and that the solution can be reached by logic alone. The same solver powers the hints in the game, so when you ask Miko for help, the hint describes a move from the very path that was used to approve the puzzle.

Making a hard puzzle can take a lot of these checks, sometimes on several fresh grids, which adds up to a noticeable fraction of a second of computing. So the Hard and Expert puzzles are prepared in advance and stored, ready to serve instantly. If you’re offline, your browser can run the same generator itself, so you can always start a new game.

How the daily puzzle is made

The Daily Challenge works a little differently, because everyone must get the same puzzle on the same day, even players who are offline.

A generator needs randomness to shuffle digits and choose which cells to remove. Computers usually get that from a pseudo-random number generator: a small recipe that turns a starting number, called a seed, into a long sequence of numbers that look random. The key property is that the same seed always gives the same sequence.

For the daily puzzle, the seed comes from the date. The text “daily:” plus the date (for example daily:2026-11-04) is turned into a number, and that number drives every random choice the generator makes. Same date, same seed, same choices, same puzzle, whether it is made on our side or in your browser. The level follows the day of the week: easy on Monday and Tuesday, medium on Wednesday and Thursday, hard on Friday and Saturday, and expert on Sunday.

What this means when you play

Knowing how puzzles are made changes how you can approach them. A well-made Sudoku is not a lottery; it is a chain of deductions someone, or something, has already checked from start to finish. A few practical takeaways:

• Don’t guess. On a properly made puzzle, there is always a logical move. Guessing tends to create errors that are hard to undo.
• Use pencil marks on harder levels. Techniques beyond singles work on candidates, so notes make them visible.
• Don’t judge by clue count. A puzzle with many clues can still need a tricky technique, and one with few can be gentle.
• Use a hint when you need one. On Sudoku.my, a hint shows the next logical step rather than just giving you a digit.

And next time you finish a puzzle, take a second to appreciate the work behind it: a complete grid, dozens of careful removals and checks, and a solving path that was waiting for you all along. If you’re new to the game, start with how to play, then try today’s Daily Challenge.

#Puzzle design#Sudoku generator#Behind the scenes