Search for the hardest Sudoku ever and you will find a dozen confident answers, most of them a newspaper headline about a single grid. The honest answer is less tidy and more interesting. Nobody has proved that any puzzle is the hardest, and nobody could, because “hardest” is not one quantity. It depends on whether you mean hardest for a rating program, hardest for a particular solving algorithm, or hardest for a person with a pencil. This guide goes through the famous contenders, what the published ratings actually say about them, and what it takes to solve one.
Is there a “hardest Sudoku ever”?
Not in any proven sense. To rank puzzles you first need a number for each one, and every number on offer comes from a particular method. Sudoku Explainer scores a grid by the most expensive technique in its own catalogue that it has to use. Other rating programs score the same grid in their own ways, and a 2012 study in Scientific Reports measured how long a puzzle keeps a continuous dynamical solver in a chaotic state. These methods tend to agree on which puzzles are extreme. They do not agree on the order at the very top.
Even the most famous constructor in this story declined to call his puzzle the last word. Introducing his 2012 grid to the Daily Telegraph, Arto Inkala said: “It is difficult to say if any one [puzzle] is the hardest or not, because I believe the hardest one is not yet discovered.” Treat every “world's hardest” label below in that spirit, as a claim about one measure at one time.
AI Escargot (Arto Inkala, 2006): the puzzle that started the headlines
Inkala, a Finnish mathematician, released AI Escargot in late 2006. Escargot is French for snail, and the forum regulars of the time also called it “Etana”, the Finnish word for the same animal. Inkala's own later book bills it as the puzzle that “became the most difficult sudoku puzzle known in 2006,” and the press picked up that framing.
The puzzle community's reaction is more instructive than the headlines. The member of the enjoysudoku.com forum who maintained its “The hardest sudokus” list noted on 4 November 2006 that Escargot was the first puzzle his own rating program could not solve, and that Sudoku Explainer 1.1 could not finish it either. Within weeks, though, the list was being ranked by Sudoku Explainer's newer ratings. In the December 2006 version Escargot sat at 10.5, below several puzzles posted by another forum member that scored 10.7. It was a landmark, and it was overtaken almost at once.
Here is the grid as that list recorded it, one row after another, with dots for empty cells. It has 23 givens and exactly one solution, which we checked with a short solving program before publishing it here:
1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..
Inkala's 2012 puzzle, and why newspapers called it the hardest ever
Six years later Inkala published a new grid on his website, and on 28 June 2012 the Daily Telegraph ran it under the headline “World's hardest sudoku: can you crack it?”, calling it “the Everest of numerical games”. That phrase is where the puzzle's nickname, Everest, comes from. Inkala told the paper that on the familiar one-to-five-star scale the puzzle “would score an eleven”, and other outlets reported that it had taken him three months to design.
The story spread worldwide within days, and it spread with an error in it. Syndicated versions said the puzzle had 23 givens. The grid the Telegraph printed has 21:
8..........36......7..9.2...5...7.......457.....1...3...1....68..85...1..9....4..
That grid, too, has exactly one solution. The “eleven stars” is a figure of speech rather than a rating: it is Inkala's own description, not the output of any published rating scale, and the article itself carried his caveat that the hardest puzzle had probably not been found yet.
The puzzle-forum contenders: Easter Monster, Golden Nugget, Platinum Blonde
While the newspapers were naming one puzzle at a time, the forum was cataloguing hundreds. A second “hardest sudokus” thread, opened on enjoysudoku.com in January 2009, kept a running database of extreme grids with their scores from several programs. A few of those grids picked up names and became the reference points for anyone testing a solver or a rating method.
- Golden Nugget. In that thread's list of top Sudoku Explainer scores, Golden Nugget is rated 11.9 by Sudoku Explainer 1.2.1. It is not alone there: three other grids in the same top five also score 11.9. When the most popular rating scale cannot separate the top four in that list, that is a good sign the question “which is hardest?” is not well posed.
- Easter Monster. Famous less for a rating than for its structure. Its givens are laid out with an unusual symmetry, and it contains a pattern the forum calls an SK loop: a large closed loop of linked cells and candidates that yields eliminations once you spot it. It became a favourite test case for writing out a complete logical solution, which we come back to below.
- Platinum Blonde. The hardest puzzle by the measure in the 2012 Scientific Reports paper “The Chaos Within Sudoku” by Mária Ercsey-Ravasz and Zoltán Toroczkai. They turned Sudoku into a continuous dynamical system and used the time it spends wandering chaotically before settling on the answer as a hardness score. Of five puzzles they tested from a published list of the hardest known, Golden Nugget among them, Platinum Blonde came out on top, and it was the most difficult puzzle for their solver among all those they tried. The authors also reported that they knew of no puzzle above 4 on their scale.
Notice that these three answers come from three different instruments. Golden Nugget leads a technique-based rating (in a four-way tie), Platinum Blonde leads a physics-style measure, and Easter Monster is famous because of how it can be solved. None of them contradicts the others, because they are not answering the same question.
Why the famous grids aren't low-clue grids
AI Escargot has 23 givens, Inkala's 2012 grid has 21, and so does Platinum Blonde: all comfortably above the 17-clue minimum. Clue count tells you very little about difficulty, and the clue-count section of our guide to how difficulty ratings work explains why, so we won't repeat it here. The short version is that a puzzle is hard because of the kind of reasoning its empty cells demand, and extreme constructors spend their givens on making that reasoning as long as possible. For the 17-clue result itself, see the mathematics of Sudoku.
What it actually takes to solve one
Pattern techniques barely dent these grids. We ran both of the grids above through the solver behind this site, which knows every technique from the Naked Single to the Swordfish. It placed exactly one digit in AI Escargot and none at all in the 2012 puzzle before it ran out of moves. What remains is the territory covered in our guide to chains, colouring and forcing logic: you take a candidate, follow what it implies through a long chain of linked cells, and eliminate it when the chain contradicts itself, or keep a conclusion that every branch agrees on.
That is still logic, and for the most famous grids people have written the logic out. In March 2008 Bob Hanson and Dave Marans published, on Hanson's St. Olaf College web pages, a solution to Easter Monster built from formal logic and chains of number pairs, and the same spring Allan Barker posted a complete logical solution to it on the enjoysudoku forum, following it with one for Golden Nugget. Those write-ups are long, careful and hard to follow. They are proof that the puzzles can be solved without guessing, not evidence that solving them is fun.
Hard but humanly fair: our own hardest puzzles
Precision Sudoku deliberately does not chase this kind of extreme. Our generator's technique set stops at the Swordfish, because everything up to that point can be trained until you recognise it on sight. So our version of hard is different: the hardest puzzles page collects the grids from our library that need the most distinct named techniques in one solve, each verified by our solver, with no chains and no guessing. If you want a puzzle that is brutal and still teaches you something you can reuse, start there. If one technique stops you, its practice page will drill it.
Frequently asked questions
What is the hardest Sudoku ever?
There is no agreed answer. AI Escargot (2006) and Inkala's 2012 “Everest” puzzle are the best known through press coverage. Among puzzle enthusiasts, Golden Nugget shares the top Sudoku Explainer score in the forum's database, and Platinum Blonde was hardest by the measure in a 2012 research paper. Which one you call hardest depends on which measure you trust.
Can a computer solve it instantly?
Yes. Difficulty for a person and difficulty for a computer are different things. A straightforward backtracking search, which fills a cell, carries on, and backs up when it reaches a contradiction, settles both of the grids printed above in a fraction of a second, including the check that each has only one solution. The famous grids are hard because the search is too deep to hold in your head, not because the arithmetic is hard.
Can a person solve it without guessing?
For the best-studied grids, yes: complete logical solutions to Easter Monster and Golden Nugget have been published. They rely on long chains and set-based reasoning far beyond the techniques most solvers use, so “without guessing” does not mean “without a lot of paper”. Trial and error will also get you there.