Sudoku Difficulty Levels Explained: What Really Changes
By the Sudoku Sagax editors · · 7 min read
Almost every Sudoku collection sorts its puzzles into difficulty levels, yet hardly any of them say what actually separates those levels. The common assumption is simple: fewer digits, harder puzzle. We counted it on our own puzzles, and that assumption turns out to be only half right.
The myth of the number of clues
When you open a Sudoku, the first thing you notice is how full the grid is. Judging difficulty from that is tempting, and for the easier levels it works. On average our puzzles have about 45, 35, 28 and 28 clues on Easy, Medium, Hard and Extreme. From Easy to Medium and from Medium to Hard, the grid gets noticeably emptier. From Hard to Extreme, the number of digits does not change at all.
Extreme is still clearly harder. The reason lies not in the amount of information but in its kind. A puzzle with 28 clues can almost solve itself if the digits are well placed, or it can demand a rare pattern at a single spot. That makes the number of clues a rough guide for the lower levels and close to useless for the upper ones.
On top of that, collections cut their levels very differently. What one newspaper calls “very hard” is “medium” in another app. Comparing levels across publishers tells you very little. The only meaningful question is what a level demands within one collection, and that can be measured.
What really sets the difficulty
A Sudoku is as hard as the hardest technique you need at its tightest spot. Our generator checks exactly that for every puzzle before it is served. On Easy and Medium, singles are enough, meaning cells with only one possible candidate or digits with only one possible place. On Hard, every puzzle needs pairs or triples. On Extreme, every puzzle needs at least one X-Wing, Swordfish, XY-Wing or XYZ-Wing. You can find all of these on our solving techniques page.
How often you actually need those hard techniques is surprisingly rare. We let our solver work through the first hundred levels of each difficulty and counted the steps that need more than a single. On Easy and Medium there are none. On Hard and Extreme there are on average 4 on Hard and 5 on Extreme, out of just under sixty steps in total. So a hard Sudoku consists almost entirely of the same simple steps as an easy one. It just has a few bottlenecks where nothing moves without the right pattern.
That explains a feeling many players know: you make quick progress, suddenly get stuck, and once you find that one step everything flows again. The bottleneck is the difficulty, not the number of empty cells.
The first minute test
There is a simple way to judge a puzzle before you really start: count how many cells you can fill straight away, without writing anything in first. That means cells where only one digit fits, and digits that have only one place left in a row, column or box.
In our puzzles that is about 24, 15, 6 and 8 cells across the four levels. On Easy, roughly two thirds of the empty cells are open from the start, and every digit you place opens more. On Medium there are far fewer, so you switch boxes more often and look more carefully. On Hard and Extreme you start with a handful of cells, and they do not get you far.
Once again the difference between Hard and Extreme stands out. An Extreme puzzle starts, on average, with a few more open cells than a Hard one. If the first minutes on Extreme feel easier than you expected, you are not imagining it. The real difference comes later, at the first bottleneck where a pair is no longer enough.
For your own play this means: if you find the first cells on a level and then keep getting stuck at the same kind of spot, you do not need an easier level, you need the next technique. If you can hardly find anything at the start, practise the order in which you scan boxes, rows and columns. Our article on common Sudoku mistakes covers that.
How long a Sudoku should take on each level
Times are a second guide. For three stars we set 5, 10, 20 and 35 minutes, without mistakes. These are not average times but targets you reach with practice. They do show the ratio between the levels well: up to Hard the time doubles with each level, and Extreme sits just under double the time for Hard.
If you need much longer, it does not mean you think slowly. Most of the time goes into the bottlenecks, or more precisely into searching for the pattern that is missing there. Spotting pairs reliably therefore saves more time on Hard than filling in digits faster. The second big time sink is incomplete pencil marks, because then you simply cannot see a pattern that is already there.
Which level is right for me?
A good level is one where you usually get through, but not without thinking. That gives a simple rule. If you solve three puzzles in a row without getting stuck, it is time for the next level. If you give up at one spot in three puzzles in a row, learn the technique that was missing there instead of going back a level.
For the step from Medium to Hard, the naked pair is the most important technique. For the step to Extreme it is the X-Wing, the simplest of the four hard patterns. Why none of our puzzles requires trial and error is explained in How to Solve Sudoku Without Guessing.
A Medium puzzle is a good place to try this. In the first minute, count how many cells you can fill straight away and compare it with the numbers above.
Frequently asked questions about Sudoku difficulty levels
How can I tell how hard a Sudoku is?
Most reliably by the techniques it needs. If you do not want to solve it to find out, count the cells you can fill in the first minute. Many point to an easy level, few to Hard or Extreme.
Are Sudokus with fewer numbers always harder?
No. Between the easier levels the two go together, between Hard and Extreme they do not. In our puzzles both have about 28 clues on average.
What is the difference between Hard and Extreme?
Hard needs pairs or triples, Extreme one of the four hard patterns such as the X-Wing. The number of clues is the same, the difference lies in a few bottlenecks.
How long should a Sudoku take?
Our target for three stars is 5 minutes on Easy and 35 on Extreme. Taking longer is normal, especially at the start.