Sudoku Rules & Difficulty Levels

Sudoku Rules & Difficulty Levels

Almost everything most people believe about sudoku is slightly wrong.

Let’s start with the name. Sudoku is short for suuji wa dokushin ni kagiru, a Japanese phrase meaning roughly “the digits must remain single.” So it’s Japanese. Except the puzzle itself was designed in 1979 by a 74-year-old retired American architect from Indiana named Howard Garns, who called it Number Place and published it in Dell Pencil Puzzles and Word Games, a magazine title so earnestly literal it borders on poetry. Number Place went mostly unnoticed for years, until a Japanese puzzle editor named Maki Kaji spotted it, tightened the grid, and renamed it. He reportedly came up with the name on his way to the horse races and gave himself less than thirty seconds to do it. (There is probably a lesson here for anyone who has ever spent hours choosing a font, but we’ll leave that alone.)

Even Garns, though, wasn’t the first. In 1895, a Parisian newspaper called La France ran a puzzle it called the carré magique diabolique, the “diabolical magic square”: a 9x9 grid where every row and column had to contain each digit once without repetition. It wasn’t quite modern sudoku (the 3x3 box rule hadn’t arrived yet), but the family resemblance is hard to miss. Several Parisian papers ran variations weekly for about a decade, then, around the First World War, the puzzles vanished entirely and stayed gone for more than sixty years. It’s worth noting, by the way, that “diabolical” remains one of the most common names for the hardest level of sudoku difficulty. Whether anyone involved realizes they’re echoing an 1895 French newspaper is an open question.

About Those Numbers

Sudoku looks like arithmetic, which is enough to put a certain kind of person off entirely. This is a shame, because the digits 1 through 9 have nothing to do with mathematics here. They’re just nine distinct symbols. You could swap them out for nine letters, nine colors, or nine slightly different drawings of the same cat, and the logic would be identical. Harder to typeset, admittedly. But identical.

And then there is the part most people never see: what happens when the puzzles get difficult. At the gentler end, sudoku is a pleasant exercise in scanning and elimination, the kind of thing you do with a coffee and no particular urgency. At the upper end, it becomes something closer to competitive problem-solving, with a vocabulary to match. Solvers talk about Naked Pairs and Hidden Triples. There is a technique called the X-Wing, which is named for the shape the pattern makes on the grid (though nobody seems to mind the other association). Beyond that, there’s the Swordfish, the Jellyfish, and the Turbot, because at some point the sudoku community decided that advanced elimination strategies should be named after marine life, and then simply kept going. None of this is necessary for enjoying a Monday morning puzzle. But knowing it exists, just past the edge of the grid, changes the way you look at even the easy ones.

What follows: the rules (there are three), how our five difficulty levels work, and answers to the questions people ask most. If you’re here for today’s puzzle, it’s on the Fun & Games page.

How to Play Sudoku

After everything above, you’d be forgiven for expecting the rules to be complicated. They are not. There are three of them, and you can learn all three in the time it takes to read the next paragraph.

A sudoku grid is nine squares by nine squares, divided into nine smaller boxes of 3x3. Some cells already have numbers filled in. Your job is to fill in the rest, so that every row contains the digits 1 through 9 exactly once, every column contains the digits 1 through 9 exactly once, and every 3x3 box contains the digits 1 through 9 exactly once. That’s it. That’s the entire game.

The best place to start is wherever the grid has already done most of the work for you. A row with seven numbers filled in only has two possibilities left. A box with eight is practically finished. Each number you place tells you something about what can go next to it, which tells you something about the row above, which narrows down the box in the corner, and so on. The whole thing is a chain reaction in slow motion. Nobody warns you about this before you start, and by the time you notice, you’re three puzzles in.

One thing worth knowing, because it trips up almost everyone at first: a puzzle with fewer numbers on the grid is not automatically harder. Difficulty has very little to do with how empty the grid looks and almost everything to do with which techniques you’ll need to find your way through it. A grid that looks intimidatingly bare might fall open in minutes. A grid that looks nearly finished might require a Swordfish. We don’t make the rules. (We do, technically, make the puzzles. But we don’t make the rules.)

Our Difficulty Levels

Our puzzles are rated using the Sudoku Explainer (SE) system, one of the most widely used standards for measuring sudoku difficulty. The SE system rates puzzles based on the techniques required to solve them: the higher the rating, the more advanced the logic involved. Each of our five difficulty levels corresponds to a specific SE rating range.

Casual (SE rating: 1.0 to 1.2)
The grid does most of the heavy lifting here. You’ll be working with straightforward elimination: scanning rows, columns, and boxes for the one number that fits. No advanced strategies needed, no pencil marks, no staring at the ceiling. If you’re new to sudoku, this is where you find out whether you like it. (You will probably like it.)

Tricky (SE rating: 1.3 to 2.5)
The puzzles start asking a little more of you. You’ll occasionally need to hold two possibilities in your head at once, and there will be moments where the next move isn’t immediately obvious. This is the level where most people first experience the particular satisfaction of a number that suddenly clicks into place after a minute of not seeing it.

Challenging (SE rating: 2.6 to 3.4)
This is where pencil marks become your friend. The grid won’t hand you answers the way it does at Casual, and you’ll need to track candidates across multiple rows and boxes before a path opens up. Think of it as the level where sudoku stops being a warm-up and starts being the main event.

Fierce (SE rating: 3.5 to 6.1)
The techniques really start to matter here. Naked Pairs, Hidden Triples, the occasional X-Wing pattern. You’ll need to think structurally about the grid rather than just scanning for gaps. These puzzles reward the kind of patience that comes from actually wanting to be there.

Diabolical (SE rating: 6.2 and above)
The deep end. Solving at this level may require techniques most casual players have never heard of, the Swordfish and Jellyfish territory we mentioned earlier. These puzzles are not interested in being approachable, and we mean that as the highest possible compliment. If you’re here, you don’t need encouragement. You need a clear afternoon.

If you still have questions, you’re in good company. Here are the ones we hear most:

FAQ

What is sudoku?
A logic puzzle played on a 9x9 grid. The grid is divided into nine 3x3 boxes, and the goal is to fill every empty cell so that each row, each column, and each box contains the numbers 1 through 9 with no repeats. The rules take about thirty seconds to learn. The puzzles take somewhat longer.

Do I need to be good at math to play sudoku?
No. Not even a little. The numbers are just labels. There is no adding, no multiplying, and absolutely no reason to have flashbacks to seventh-grade pop quizzes. It’s pure logic, start to finish. If you can tell nine things apart from each other, you’re qualified.

How long does it take to solve a sudoku puzzle?
Depends on the puzzle and depends on you. A Casual grid might take ten unhurried minutes. A Diabolical one might take the better part of an afternoon, and we say that with genuine respect for anyone who sits down to one. There is no timer, no opponent, and no one watching. Take as long as the puzzle needs.

What is the Sudoku Explainer (SE) rating system?
It’s a standardized system for measuring how difficult a puzzle is, based on the techniques required to solve it rather than anything subjective like “how hard does this feel.” A higher rating means the puzzle demands more sophisticated solving strategies. We use it to define our five difficulty levels, which means our labels aren’t just vibes. They correspond to specific rating ranges. The details are in the difficulty levels section above.

What difficulty level should I start with?
Casual, unless you already know your way around a grid. It’s a satisfying solve at any experience level, and it’ll tell you fairly quickly whether you want more resistance. If you do, Tricky is the next step. After that, the levels will find you.

What’s the difference between Fierce and Diabolical?
Patience, mostly. Both require advanced techniques and a clear head. Fierce is demanding and deeply satisfying for experienced solvers. Diabolical is all of that, but more so, and for longer. If Fierce is comfortable, Diabolical is ready when you are.

What’s the best strategy for a beginner?
Look for the most crowded row, column, or box and work from there. The fewer empty cells, the fewer possibilities you need to consider. Place what you’re sure about, and let each answer narrow down the next one.

What should I do if I get stuck?
Stop looking at the grid. Sudoku is one of the best possible arguments for taking a break: the answer you couldn’t find after twenty minutes of focused concentration will often appear within seconds of coming back from making a cup of tea. Nobody fully understands why this works, but it works so reliably that it almost qualifies as a solving technique. (If the sudoku community ever names it, we’d like to suggest the Kettle.)

A French parlor puzzle, an American architect, a Japanese editor with thirty seconds and a horse race to get to, a grid that has nothing to do with math, and a community that names its advanced techniques after fish. Sudoku is never quite what it looks like from the outside. The easy ones are more interesting than they seem. The hard ones are deeper. And the first one is waiting for you on our Fun & Games page, ready to prove it.