Sudoku Generator
Four difficulties, one solution each, answer key included.
Every puzzle is checked to have exactly one solution before it is shown, so the answer key is never ambiguous.
How the Sudoku Generator works
Pick a difficulty and how many you want, and the puzzles are built in your browser rather than pulled from a fixed library, so you are not working through the same hundred grids everyone else printed. Every puzzle is checked to have exactly one solution before it appears, which is the difference between a sudoku and a grid with holes in it. One, two, four or six to a page, with an answer key on the back.
Also known as: printable sudoku puzzles · sudoku maker with answers · free sudoku to print · hard sudoku printable · sudoku puzzle generator
One solution, and why it is not automatic
A sudoku is not a grid with holes in it. The defining property is that exactly one arrangement of digits satisfies the constraints, and that property is easy to lose. Take a completed grid, remove twenty cells at random, and there is a fair chance you have produced something with two answers or ten. It will look identical to a real puzzle. It will solve smoothly for twenty minutes. Then it will reach a point where two digits are equally defensible, and whichever the solver picks, the printed answer key disagrees with about half of them.
Avoiding that means checking rather than hoping. Every time a cell is emptied here, the grid is handed to a solver that counts how many ways it can be completed. If the answer is anything other than one, the digit goes straight back and a different cell is tried. The counting stops as soon as it finds a second solution, because proving there is more than one is all the check needs and counting the rest of a sparse grid can run into the millions.
This is also why the puzzles bottom out around twenty-four clues rather than seventeen. Seventeen is the proven minimum, established by exhaustive search in 2012, but reaching it requires abandoning the symmetric layout that printed sudoku has used since the beginning. Removing cells in rotationally symmetric pairs means a pair that would break uniqueness blocks both of its cells, and the grid stops emptying sooner. The trade is a few more clues in exchange for a puzzle that looks deliberate rather than scattered.
What actually makes a sudoku hard
Most generators grade by counting clues, and it is close to meaningless. A twenty-six clue grid can fall to nothing but the simplest technique while a thirty-two clue one needs a pattern most solvers have never heard of. Clue count tells you how much of the page is blank, not how hard the reasoning is.
The reasoning has a well-known ladder. A naked single is a cell with one candidate left, and spotting it needs no more than checking a row, a column and a box. A hidden single is a digit with only one home left in a unit, which needs you to think about the digit rather than the cell. Above those sit the eliminations: a pointing pair, where a digit trapped in one row of a box can be struck from the rest of that row, and its mirror the locked candidate. Then the pairs, then patterns like the X-wing, where a digit confined to the same two columns in two different rows must take one of each. Past that you are following chains, and most people reach for a pencil and a guess.
Difficulty here is graded by running a solver that knows exactly that list and nothing else, then recording the hardest rung it had to stand on. So 'hard' means hard to reason about, not sparse.
Why the easy band is split by clue count
Grading by technique alone sounds complete and turned out not to be, which only became clear from measuring it. Sudoku grids are close to bimodal: they either fall to naked and hidden singles, or they need a chain. The techniques in between are real and people use them, but they are rarely the thing standing between a solver and the next digit. Across twenty-five grids dug as deep as uniqueness allowed, sixteen needed nothing past singles and four needed more than an X-wing, which leaves five spread across the entire middle.
A generator grading purely on technique therefore cannot honestly offer four buttons. Ask it for hard and roughly half the time it hands back something that only needs singles, because no version of that grid ever needed anything more.
The other half of the work is the searching, and it is the half a solver actually feels. Finding a naked single among thirty blanks is scanning. Finding one among fifty-five is a hunt, even though the logic is identical. So the singles-only band is split by clue count, which is how printed sudoku has been graded since long before anyone wrote a solver: easy keeps thirty-four clues or more, medium runs from twenty-eight, and below that a singles-only grid is genuinely hard work whatever the technique list says.
Printing a set worth keeping
Six to a page is the density that suits a commute or a waiting room, and the grids stay large enough to write in with a normal pen. Four is comfortable for most people. Two is the right choice if you are photocopying for a class, because a photocopier loses about ten percent of the fine detail and thin grid lines are the first thing to go. One to a page is for anybody working with a pencil and a rubber, which is what expert puzzles want.
The answer key prints on its own sheet at the end rather than at the foot of each puzzle, for the obvious reason. On it, the digits that were printed on the puzzle are set in bold and the ones you were meant to work out are lighter, so the key reads as a solution rather than as another puzzle.
The generator is seeded, which means reloading the page gives you the same puzzles rather than a fresh set. That sounds like a limitation and is the opposite: it means a lost second page can be reprinted and still match the answer key you already have. Press the button when you actually want different puzzles.
Frequently asked questions
Does every puzzle have only one answer?
Yes, and it is checked rather than assumed. Each time a pair of cells is removed the grid is re-solved to see whether a second answer has appeared, and if one has, the cells go back. A puzzle with two solutions forces a guess that both answers justify, which makes the answer key wrong for whoever guessed the other way.
What makes a sudoku hard?
Two things, and most generators only count one. The first is which techniques you need: naked singles are the easiest, then hidden singles, then pointing pairs and locked candidates, then patterns like the X-wing, then chains. The second is how much blank grid you have to search to spot them. A 34-clue puzzle and a 25-clue puzzle can need identical techniques and feel nothing alike.
How is the difficulty decided here?
By solving each puzzle with a solver that only knows a fixed list of human techniques and recording the hardest one it needed, then splitting the easiest band by clue count. Counting clues alone, which is the common shortcut, is close to meaningless: a 26-clue grid can fall to nothing but naked singles while a 32-clue one needs locked candidates.
Can I print several at once?
Up to twelve, at one, two, four or six per page, with page breaks landing where they should. The answer key prints on its own sheet at the end so you can keep it face down until someone gives up.
Will I get the same puzzles if I reload?
Yes. The generator is seeded, so a reload reprints the identical sheet rather than a new one, which matters when you have lost page two. Press 'New puzzles' when you actually want different ones.
What is the fewest clues a sudoku can have?
Seventeen. That was proven by exhaustive computer search in 2012, and no 16-clue puzzle with a unique solution exists. Puzzles here sit between roughly 24 and 35 clues, because symmetric grids bottom out higher than that and a 17-clue puzzle is a curiosity rather than something to solve on a train.