---
title: Why computers are good at making sudoku — a generator that proves the solution is unique and grades difficulty by the techniques people use, at five levels you can solve right here
url: https://oosioo.com/en/p/%EC%8A%A4%EB%8F%84%EC%BF%A0%EB%8A%94-%EC%99%9C-%EC%BB%B4%ED%93%A8%ED%84%B0%EA%B0%80-%EC%9E%98-%EB%A7%8C%EB%93%A4%EA%B9%8C
date: 2026-10-23T12:49:11+00:00
author: SYSOP
summary: Most game levels need a person to play them to know whether they can be beaten or are fun. Sudoku is different: checking an answer takes 27 looks, uniqueness can be proven by search, and difficulty can be measured by playing human solving techniques from easiest up. A machine can play both maker and sceptic. So I built a generator for five levels, Easy to Evil, with a solving screen on the same page. Across 3,000 random puzzles the clue count had almost nothing to do with difficulty, and Hard took 23 tries to get one. I also graded today’s three New York Times puzzles. An AI asked to make puzzles without tools handed in only the two easy ones and declined the rest as unprovable.
---
# Why computers are good at making sudoku — a generator that proves the solution is unique and grades difficulty by the techniques people use, at five levels you can solve right here

![The sudoku generator screen. Along the top are Easy, Medium, Hard, Expert and Evil buttons and “Puzzle no. X-363101”. The 9×9 grid in the middle has small candidate digits filled in; r7c5 has an orange outline and all of row 7 is shaded pale yellow. The hint panel on the right reads “Finding the digit for r7c5 · 2 steps”: 1. XY-Wing: pivot r9c6 (2/6) with pincers r7c5 (6/8) and r9c8 (2/8), remove 8 from cells that see both pincers; 2. Hidden single: in row 7, 8 can only go in r7c5](/uploads/874250eeb747b64c.webp)

When a game studio builds a level, a person plays it. Can it be finished? Is it too hard? Is it fun? You can compute a jump distance, but “fun” has no right answer. So you fix it, play it again, and fix it again.

Sudoku is different. The rules fit on one line: every row, every column and every 3×3 box holds 1 to 9 once each. To check an answer you only look at 27 places. A good sudoku must have exactly one solution, and a computer can prove that too by trying every way to fill the blanks. It can even measure how hard a puzzle is: play the techniques people use, easiest first, and see which was the hardest one needed to reach the end.

In other words, **it is a game where a machine can play both the maker and the sceptic.** So can you really get puzzles at any difficulty with a single click? This time I built that.

## What I wanted to do

1. Briefly trace how sudoku got its present shape, and how puzzle games like it are changing.
2. Work out why puzzles like sudoku are easier to generate automatically than ordinary games.
3. Build a generator for five levels: Easy, Medium, Hard, Expert and Evil. For each puzzle, prove that the solution is unique and record which techniques it needs.
4. Run the generator 3,000 times to test the common belief that fewer clues means harder.
5. Put a screen on the same page where you can solve the puzzles right away, with hints that show the next move and the reason for it.
6. Ask an AI to make puzzles without tools, and feed those puzzles to the generator’s verifier.

I left the research on history and recent trends to an AI agent. I told it to prefer papers, official company announcements and original publications, and to mark anything it couldn’t confirm as unconfirmed.

## 47 years of sudoku

![Timeline of 47 years of sudoku. Puzzles & media: 1979 Dell Magazines “Number Place” (Howard Garns), 1984 Nikoli brings it to Japan as “Sudoku”, 1986 Nikoli places clues symmetrically, 2004 The Times runs it (Wayne Gould’s generator), 2005 UK craze and live TV “Sudoku Live”, 2012 the “world’s hardest” puzzle (Inkala). Math & algorithms: 2000 Knuth, “Dancing Links”, 2003 generalized sudoku is NP-complete (Yato & Seta), 2005 about 6.67×10^21 full grids (Felgenhauer & Jarvis), 2011 difficulty checked against human solve times (Pelánek), 2012 17 clues proven minimum (McGuire et al.). Screens & community: 2017 YouTube channel Cracking the Cryptic launches, 2020 two-clue “Miracle” variant goes viral, 2022 NYT buys Wordle, 2023 NYT Connections and Puzzmo, 2024 NYT Strands and LinkedIn games, 2025 LinkedIn Mini Sudoku (with Nikoli). AI: 2025 Sudoku-Bench, LLMs under 15%; HRM and TRM, small models at 55% and 87%; GPT-5 (high) 33% on variants; 2026 a small dedicated model reports 100%](/uploads/ee6399577f9b3c53.webp)

**The name came from Japan, the rules from America.** In 1979 the American puzzle magazine Dell printed a puzzle called “Number Place”. The magazine named no author, but in 2005 puzzle editor Will Shortz noticed that a retired architect, Howard Garns, was listed as a contributor only in the issues that carried it, and it is now credited to Garns. In 1984 the Japanese puzzle company Nikoli introduced it under a long title, 「数字は独身に限る」 (“the digits must be single”), and the short form of that title is “Sudoku” (数独). In 1986 Nikoli added a rule that **clues are placed symmetrically**. It has nothing to do with solving; it is there to look good. My generator follows it too.

**Computers took it worldwide.** Wayne Gould, a retired judge in Hong Kong, came across a sudoku book in a Tokyo bookshop in 1997 and spent six years writing a program to create puzzles and grade their difficulty. He took it to The Times in Britain, which started running the puzzle in November 2004. By 2005 Britain was gripped by sudoku; there was even a live TV puzzle show. The argument started then too. Nikoli still champions “hand-made puzzles” on its official site, where it says: “You may invent a program to create Sudoku puzzles, but you will never create Nikoli’s Sudoku puzzles.” Gould’s answer: “But a puzzle is a puzzle, and if it’s well done, a handmade puzzle is the same as a computer generated one.”

**Mathematicians counted the grids.** In 2005 Felgenhauer and Jarvis calculated that there are 6,670,903,752,021,072,936,960 completed 9×9 grids (about 6.67×10^21). If you count grids that are essentially the same, say with digits relabelled or the grid rotated, as one, there are about 5.47 billion. In 2012 an exhaustive search proved that no sudoku with only 16 clues exists: **a sudoku with a unique solution needs at least 17 clues.** Generalized sudoku on an n²×n² grid was proven NP-complete in 2003. But the 9×9 grid is finite, and a computer solves it in tens of milliseconds.

## Why sudoku is easy to generate

![The actual steps of the sudoku generator compared with making a level for an ordinary game. Left: 1 make a full grid (place digits in random order and back up when stuck, about 1 ms) → 41 clue removals (two cells mirrored through the centre at a time, in random order): 2 verifier, one solution? (two or more → put both cells back), 3 grader, can a person solve it? (harder than the target → put back) → a puzzle with 22–40 clues left → 4 final grade, the level we wanted? (if not, back to 1; Hard takes 23 puzzles on average) → output. Right: build → can it be beaten? (people) → is it fun? too hard? (people) → fix → test again (hours to weeks per loop). Table below: is the answer right? sudoku checks 27 rows, columns and boxes, while an ordinary game often has no right answer / only one answer? proven by search / difficulty: measured by techniques needed vs playtesting / one loop: milliseconds vs hours to weeks](/uploads/d127535a95d415c1.webp)

Research on generating game content automatically splits the approaches roughly in two: build it once by rule, or **build it, test it, and throw it away if it fails** (generate-and-test). In 2011 Togelius and colleagues divided the “test” in the second approach into three kinds: when the features can be scored directly, when an artificial player has to play it to know, and when a person has to play it to know.

A platform game level is usually one of the last two. Whether it can be finished takes a bot run; whether it’s fun takes a person. Sudoku is the first kind. A search program proves the solution is unique, and a list of solving techniques measures difficulty. One test takes milliseconds, so if you don’t like the result you can throw it away and start over. **However sloppy the maker, if the sceptic is exact, the output is exact.**

Building that sceptic well is the real work, of course. Simon Tatham, known for his free collection of 40 puzzles, set this standard in his developer notes: every randomly generated puzzle must be solvable **without guessing**. And while generating puzzles with a solver makes a unique solution easy to guarantee, the puzzles only get as hard as the techniques the solver knows. Sudoku was the case in point: a simple solver produced qualitatively easier puzzles, so its solver had to be made far more advanced than the others.

So I split the generator into two parts.

- **The verifier** counts solutions. It tries digits in the blank with the fewest candidates first and backs up when stuck. It stops the moment it finds a second solution, because all it needs to know is “one or not”.
- **The grader** solves like a person. It finds the easiest available technique, plays one move, and keeps going until the grid is full, noting which techniques it used and how often. The hardest technique it needed is the puzzle’s difficulty. I grouped the techniques into five tiers.

| Tier | Techniques | In one line |
|---|---|---|
| 1 Singles | Last free cell, hidden single, naked single | In this row, 7 can only go here / only 4 is left in this cell |
| 2 Intersections | Pointing, claiming | In this box, 7 only sits on row 3, so remove 7 from row 3 in the other boxes |
| 3 Pairs | Naked pair/triple, hidden pair/triple | If two cells hold only {2, 5}, remove 2 and 5 from the rest of that row |
| 4 X-Wings & wings | X-Wing, Swordfish, XY-Wing, XYZ-Wing | If 8 in two rows is confined to the same two columns, remove the other 8s from those columns |
| 5 Assume and contradict | Trial | Put 3 in this cell and keep playing singles; if the grid breaks, it isn’t 3 |

The fifth tier is contentious. Many puzzle fans call “try it, and erase if you get stuck” a guess. That’s why I made it its own level, Evil. After the assumption it only allows singles, and puzzles that even this can’t crack (puzzles that genuinely need a guess) are never produced.

Here is how a puzzle at a given level is made. Starting from a full grid, remove two cells at a time, mirrored through the centre. After each removal, the verifier checks the solution is still unique and the grader checks the puzzle hasn’t become harder than the target. If either fails, put the two cells back. Once all 41 pairs have been tried, the grader solves the whole grid, and if it isn’t the target level the puzzle is thrown away and the process starts from scratch. Easy and Medium stop once 36–40 and 29–32 clues are left.

## What 3,000 puzzles showed

First I looked at what the generator makes on its own. With no difficulty target, I made 3,000 puzzles by removing clues for as long as the solution stayed unique.

![Left bar chart: what was the hardest technique needed? Singles 67.6% (2,027 puzzles), Intersections 7.5% (224), Pairs 3.4% (101), X-Wings & wings 4.3% (129), Assume & contradict 17.3% (519). Right box plot: yet the clue count barely changes. In all five tiers the clue count spans roughly 24 to 31, with means of 27.7, 27.4, 26.9, 27.5 and 27.4](/uploads/8131009b72a7265f.webp)

Three things stood out.

**First, most are easy.** Even with clues removed until no more could go, seven puzzles in ten (67.6%) fell to singles alone. Only 3.4% needed pairs. Yet 17.3% needed assume and contradict. The middle difficulties are the rare ones.

**Second, the clue count is not the difficulty.** The mean clue count of the five tiers is nearly identical, 26.9 to 27.7. There were easy puzzles with 22 clues and Evil ones with 31. Human data says the same. In 2011 Pelánek collected average solve times for about 1,800 puzzles from two sudoku sites (one site averaged 1,307 solvers per puzzle) and compared several difficulty measures. The correlation between clue count and solve time was only 0.25–0.27; a score based on the hardest technique needed reached 0.70–0.86. I ran a 17-clue puzzle that is often used as an example through the grader, and it too fell to singles all the way.

**Third, a puzzle with a unique solution comes out every time.** All 3,000 puzzles passed the verifier, and none required guessing. Each puzzle took 41 attempted removals, of which 14 on average were put back. The reason was always “the solution is no longer unique”.

I also ran today’s (October 23) three New York Times sudokus through the same grader. I report only the results, not the puzzles.

| NYT today | Clues | Grader result |
|---|---|---|
| Easy | 38 | Singles only |
| Medium | 23 | 1 intersection |
| Hard | 25 | 1 pair (6 intersections) |

The Hard has more clues than the Medium. And the three puzzles land exactly one in each of my tiers 1, 2 and 3. It’s one day’s observation, but the idea of grading by the techniques needed rather than by clue count looks the same.

## How many puzzles each level threw away

Next I made 200 puzzles at each of the five levels.

![Left: puzzles made to get one at the right level. Easy 1.0, Medium 1.0, Hard 23 (nine in ten within 54), Expert 15 (within 33), Evil 5.3 (within 11). Right: time taken (laptop, Node.js). Easy 1.9 ms, Medium 2.9 ms, Hard 95 ms (within 221 ms), Expert 63 ms (within 140 ms), Evil 26 ms (within 51 ms)](/uploads/09523ee3f34a81da.webp)

Easy and Medium always finished with the first puzzle. Hard took the longest: on average it made 23 puzzles and threw away 22, and with bad luck it went to 114. Even so, it averaged 0.1 seconds, and the slowest one took under half a second. Evil coming out faster than Hard is just the previous chart again: 17% of fully stripped puzzles are already Evil.

This is where “easy to generate” becomes clear. A sudoku generator doesn’t cleverly **build** good puzzles. It simply makes a lot and throws them away accurately. Because the rejection criterion is exact, throwing away a lot costs nothing.

## When an AI makes the puzzles itself

What if, instead of the generator, you ask an AI to make puzzles directly? I started a fresh AI agent and told it, without using tools (no code execution), to produce one puzzle at each of the five levels, with solutions.

The agent **produced only two, Easy and Medium.** It declined the other three, saying it “could not prove by hand that a puzzle needing hard techniques has a unique solution.” For the Medium, it wrote that it had found on its own that its first attempt had two solutions and had added a clue. I fed both puzzles to the verifier.

| | Easy | Medium |
|---|---|---|
| Clues | 45 | 36 |
| Number of solutions | 1 (correct) | 1 (correct) |
| Difficulty the AI claimed | Naked singles only | Needs “pairs” twice |
| Grader result | Singles only | **Singles only** |

Both solutions were correct. But the claim that the Medium “needs pairs” was wrong: hidden singles solve it to the end. And both solution grids were the textbook pattern of “shift each row by three” with the digits relabelled. The agent said so itself.

This matches recent research. In Sudoku-Bench, released by Sakana AI in 2025, the latest large language models solved under 15% of 100 variant sudokus without tools. In an update that October, GPT-5 (high) reached 33% and became the first to solve a 9×9 variant. Small models trained only on sudoku, by contrast, are strong. In 2025 HRM (27 million parameters) scored 55% on a set of very hard puzzles, and TRM (5 million) that followed scored 87.4%. General-purpose reasoning models scored 0% on the same set. In 2026 a dedicated model with 800,000 parameters reported 100%. The evaluations differ, so the numbers aren’t directly comparable.

To sum up: **AI is useful for making puzzles that look plausible, but it can’t vouch on its own for uniqueness or difficulty.** This agent knew it couldn’t vouch, and stopped. That was the best part of the experiment. The vouching is done by a verifier a few hundred lines long. An AI wrote this generator too, but whether a puzzle goes out is decided by the verifier, not the AI.

## How games like this are changing

**One a day, and share it.** In January 2022 The New York Times bought Wordle for a price “in the low seven figures”. The announcement said NYT Games had been played more than 500 million times in 2021. NYT went on to launch Connections (2023) and Strands (2024), and said Strands was played more than 1.5 billion times in 2025. In May 2024 LinkedIn added puzzles such as Queens, and in August 2025 it launched a 6×6 “Mini Sudoku” with Nikoli and Thomas Snyder, three-time World Sudoku Champion. By LinkedIn’s figures, 86% of players came back the next day. In 2023 Zach Gage’s puzzle site Puzzmo launched, and that December the American newspaper group Hearst bought it. They share three things: everyone gets the same puzzle once a day, results are compared with friends or colleagues, and it’s over in a few minutes.

This model suits generators. You need a new puzzle every day, so machine-made has the edge. On the other hand, because everyone solves the same puzzle and shares results, the quality of each puzzle stands out. Like Mini Sudoku, which gets harder through the week, you need to be able to order “this hard today” from the generator precisely. It’s also interesting that Nikoli, the champion of hand-made puzzles, is listed as a partner on it.

**Variants with one extra rule grew the scene.** Cracking the Cryptic, a YouTube channel started in 2017 by two British puzzle experts, became widely known in May 2020 for a video solving “Miracle”, a variant sudoku with only two clues. It now has over 700,000 subscribers. Variants that add one rule at a time, like digits on an arrow summing to the circle or digits increasing along a thermometer, are mostly hand-made, because the first breakthrough (the break-in) has to be beautiful. That is also why variant sudoku works as a test for AI: memorized patterns won’t solve it; you have to find that puzzle’s own break-in.

So puzzle games now go two ways. Where you need **lots, daily, and exact**, generators take over; where you need **beauty never seen before**, people still make them. A generator can’t directly build the “solving experience” you want. It can only draw many and pick. What Nikoli describes as the communication between setter and solver still lies outside the generator.

## Play it yourself

Below is the generator and solving screen I built. Pick a level at the top and a puzzle is made on the spot. Tap a cell and enter digits with the number pad below or the keyboard. Turn on “Notes” to enter small candidate digits; “Fill notes” writes in every possible candidate for the current grid. If you’re stuck, press “Hint”. It shows, in order, the reasoning needed to find the next digit.

```map /embed/sudoku-2026-en.html 16:10
The sudoku generator and solving screen. Pick a level from Easy to Evil and it makes a puzzle on the spot, checks the solution is unique, and shows the grader’s solving record beside it. Hints give the next move with the reason for it.
```

On a narrow screen, **[open it in a new window](/embed/sudoku-2026-en.html)**. Share a puzzle’s “Puzzle no.” with a friend and you can both solve the same puzzle; the same number always produces the same puzzle (and the same puzzle as the Korean version of this page). “Behind this puzzle” on the right shows how many puzzles were thrown away to get this one, and how many times clues were removed and put back. Press “Watch how this puzzle was made” to see digits disappear from a full grid and come back the moment the solution would stop being unique. In the “Puzzle checker” you can paste an 81-character puzzle from a newspaper or app to see whether its solution is unique and which techniques it needs. The 2012 “world’s hardest” puzzle is in there too.

![“Behind this puzzle” on the generator screen. A Hard puzzle, Puzzle no. H-172560. “What the generator did”: 26 clues, 53 full grids generated, 41 clue removals tried, of which 28 removed and 13 put back, 1 solution (verified), time 198 ms. “To get a Hard puzzle the generator built 53 grids from scratch. The first 52 were solved through and thrown away at the wrong difficulty. A clue is put back when removing it leaves two solutions or makes the puzzle too hard. This one needs techniques up to Pairs.” Below, “How the grader solved it” bars: Singles 55, Intersections 5, Pairs 1, X-Wings & wings 0, Assume/contradict 0. 61 moves in all](/uploads/c855eafa9d18e7c3.webp)

## Where it went wrong

- **The “world’s hardest” puzzle had three solutions.** I dropped a digit while copying it in for testing. The verifier immediately said “3 solutions”. Copied correctly, it had one. By eye I couldn’t spot one missing character out of 81. Building the verifier first paid off from the very start.
- **Empty rows went flat.** If one of the nine rows had no digits at all, that row shrank to half height, because I’d let cell height follow the content. I noticed when the first Medium puzzle I loaded had an entirely empty fifth row. I pinned all nine rows to the same height.
- **Hints listed irrelevant reasoning.** The grader looks for the easiest technique anywhere on the grid. So a hint for r2c1 picked up four intersections in other boxes and grew to seven steps. Candidate eliminations are true in any order, so I made it drop them one at a time and discard any whose removal still lets the target cell be solved. Measured on 80 reasoning hints from 40 hard puzzles, the average fell from 4.1 steps (longest 11) to 2.2 (longest 5). After the change I drew 2,129 hints from 40 puzzles and checked them against the solutions; none was wrong.
- **A hint sentence lied.** I wrote the explanation of “naked single” as “the other eight digits are already in the same row, column and box, so only 4 is left.” But a naked single that appears after an elimination step is left alone because of the removed candidates, not the placed digits. I changed it to “the only candidate left is 4.”
- **The Korean hints wrote “2이(가)”.** Korean particles after a word change with the sound of its last syllable, and I had lumped them together as “이(가)”. Digits are read as il, i, sam…, so I made those ending in a consonant (1, 3, 6, 7, 8) take 이 and the rest take 가. (The English version simply has no such problem.)
- **Hard was the rare one.** I first expected Evil to take longest. In fact puzzles that need exactly pairs are the rarest at 3.4%, so Hard took longest. You could aim at Hard directly, say by starting from easy puzzles and removing fewer clues, but I didn’t try. A tenth of a second is worth waiting for.

## Why one click works here

Sudoku’s rules are one line, and that one line separates right from wrong completely. So the conditions of a “good puzzle” split into three: does it follow the rules, is the solution unique, and is it as hard as wanted. A program judges all three. With exact judgement, the maker can be careless: fill at random, remove at random, throw away what fails.

Ordinary games are hard because this judge doesn’t exist. No program yet measures “is it fun”. Put the other way round, when you have an AI make something, **if you can first build a machine to judge the result, the job becomes one click.** The AI agent in this experiment stopped in front of the hard puzzles because it had no judge.

## If you want to try this

- **Build the verifier first.** Before the generator. A program that counts solutions is about a hundred lines. With it, you can trust a puzzle whether an AI or a person made it.
- **Measure difficulty by technique, not clue count.** Clue count has almost nothing to do with difficulty. Build a grader that plays techniques easiest first, and take the hardest technique as the difficulty.
- **Make lots, throw lots away.** Building exactly the puzzle you want is hard. Making and discarding until the right one turns up is easier and faster. At a few milliseconds per puzzle, you can throw away dozens before anyone notices the wait.
- **Keep the seed number.** If the same number gives the same puzzle, friends can solve the same one, and you can call up a problem puzzle again to fix it.
- **Tell the AI to stop if it can’t vouch.** This agent didn’t hand over puzzles it couldn’t prove. That stop was more useful than three made-up hard puzzles.

## What it can’t do

- **It doesn’t make puzzles that need guessing.** The grader knows assumptions only as far as following them with singles. Puzzles that need deeper reasoning, like the “world’s hardest” one, the grader can’t finish, so the generator never produces them. None turned up among the 3,000 either.
- **The five levels weren’t validated with people.** The grader measures which techniques are needed. As Pelánek’s work shows, how hard a puzzle feels also depends on how long you wander before finding the next move. Two Medium puzzles can take very different times.
- **No variant sudoku.** Rules like killer, thermometer or arrow aren’t in. Extending the verifier for new rules is easy, but building a list of human techniques for those rules is a big job of its own.
- **It can’t make a “beautiful puzzle”.** It keeps the symmetry rule, but it has none of the setter’s intent or the taste of a first break-in that Nikoli talks about. A generator only draws many and picks.
- **Progress stays in this browser only.** Inside the post, progress may not be saved. Write down the puzzle number and you can always regenerate the same puzzle.

The argument between Nikoli and Wayne Gould hasn’t ended in twenty years. But building one changed the question a little for me. Before “can a computer make a good puzzle?” comes “can a computer judge whether a puzzle is good?” Sudoku is one of the rare games where that judgement works, which is why it became one click.

### If you enjoyed this, please leave a comment.

## Sources

- Origins: [Nikoli, Sudoku](https://www.nikoli.co.jp/en/puzzles/sudoku/), [Why hand made?](https://www.nikoli.co.jp/en/puzzles/sudoku/why_hand_made/), Ed Pegg Jr., [Sudoku Variations](http://www.mathpuzzle.com/MAA/41-Sudoku%20Variations/mathgames_09_05_05.html) (MAA, 2005), [Sudoku](https://en.wikipedia.org/wiki/Sudoku) (secondary), Wayne Gould: Will Shortz, [TIME 100 (2006)](https://content.time.com/time/specials/packages/article/0,28804,1975813_1975838_1976198,00.html), Gould’s remark: [The Globe and Mail 2005-08-02](https://www.theglobeandmail.com/arts/the-crack-cocaine-of-games/article18242760)
- Math: Felgenhauer & Jarvis, Enumerating possible Sudoku grids (2005, [explainer](https://pi.math.cornell.edu/~mec/Summer2009/Mahmood/Count.html)), [OEIS A109741](https://oeis.org/A109741), McGuire, Tugemann, Civario, [There is no 16-Clue Sudoku](https://arxiv.org/abs/1201.0749), Yato & Seta, [Complexity and Completeness of Finding Another Solution](https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_5_1052/_p) (IEICE, 2003), Knuth, [Dancing Links](https://arxiv.org/abs/cs/0011047) (2000)
- Difficulty: Pelánek, [Difficulty Rating of Sudoku Puzzles by a Computational Model](https://www.fi.muni.cz/~xpelanek/publications/flairs-sudoku.pdf) (FLAIRS 2011), [HoDoKu solving techniques](https://hodoku.sourceforge.net/en/docs_solv.php), [generation](https://hodoku.sourceforge.net/en/docs_cre.php), “world’s hardest sudoku” [ABC News 2012-06-29](https://abcnews.com/blogs/headlines/2012/06/can-you-solve-the-hardest-ever-sudoku) (the creator’s claim)
- Generation: Togelius et al., [Search-based Procedural Content Generation](http://julian.togelius.com/Togelius2011Searchbased.pdf) (IEEE TCIAIG, 2011), Simon Tatham, [How to write a new puzzle](https://www.chiark.greenend.org.uk/~sgtatham/puzzles/devel/writing.html), [Solo](https://www.chiark.greenend.org.uk/~sgtatham/puzzles/doc/solo.html)
- One a day: NYT [Wordle acquisition](https://www.nytco.com/press/wordle-new-york-times/), [Strands figures](https://www.nytco.com/press/introducing-strands-sports-edition-a-new-daily-sports-puzzle-from-the-athletic/), [NYT Connections](https://en.wikipedia.org/wiki/The_New_York_Times_Connections) (secondary), LinkedIn [Mini Sudoku announcement](https://news.linkedin.com/2025/linkedin-announces-minisudoku-), [games list](https://www.linkedin.com/help/linkedin/answer/a6863543), Puzzmo [Axios 2023-10-20](https://www.axios.com/2023/10/20/puzzmo-hearst-zach-gage-new-york-times), [PocketGamer.biz](https://www.pocketgamer.biz/zach-gage-and-orta-theroxs-puzzle-platform-puzzmo-acquired-by-hearst-newspapers)
- Variants: [Cracking the Cryptic](https://en.wikipedia.org/wiki/Cracking_the_Cryptic) (secondary), Miracle [IPS 2020-05-19](https://ipsnews.net/business/2020/05/19/this-25-minute-video-is-the-most-riveting-sudoku-puzzle-you-will-ever-watch-6/?amp=1) (secondary)
- AI: Sakana AI [Sudoku-Bench](https://sakana.ai/sudoku-bench/), [paper](https://arxiv.org/abs/2505.16135), [GPT-5 update](https://pub.sakana.ai/sudoku-gpt5/), [HRM](https://arxiv.org/abs/2506.21734), [TRM](https://arxiv.org/abs/2510.04871) (Table 4), [Augmented HRM](https://arxiv.org/abs/2601.10679), [Lattice Deduction Transformers](https://arxiv.org/abs/2605.08605)
- Clue counts and grades for today’s three NYT puzzles come from feeding the 2026-10-23 [NYT Sudoku](https://www.nytimes.com/puzzles/sudoku/easy) page data to this post’s grader (puzzles not reproduced)
- The generator, verifier, grader, solving screen, 3,000-puzzle statistics, AI agent experiment and charts were all made for this post