Sudoku history and math
- History of Sudoku — The history of Sudoku: French newspaper grids, Dell's Number Place in 1979, Nikoli in Japan and the 2004 newspaper launches, with sources and open questions.
- Latin squares and the math behind Sudoku — Every Sudoku solution is a Latin square. Euler's 36 officers problem, how all valid grids were counted, and the symmetries that keep a disguised puzzle valid.
- How many Sudoku puzzles exist, and the 17-clue result — How many Sudoku grids and puzzles exist, what essentially different means, and how a computer search proved that no puzzle with 16 clues has one solution.
- Sudoku variants through history — How Sudoku variants developed: other grid sizes, extra rules, killer's arithmetic and overlapping grids, with dates only where a source supports them.
These four pages cover where Sudoku came from, the mathematics behind it, how many puzzles exist and how the variants developed. Every claim is tied to a source that was opened while writing, each page ends with a list of sources, and wherever the sources disagree or say nothing, the page says so instead of choosing a convenient answer.
What is in the history section?
The history of a puzzle is easy to get wrong. Popular accounts repeat the same few stories, some of them contradicted by better sources, and numbers about “how many Sudokus there are” often mix up grids with puzzles. This section takes a stricter approach. Each page states what its sources say, names the sources, flags disagreements and leaves out anything it could not check. The four pages are written to be read in any order, and each one ends with a Sources list giving the title, the publisher or journal, the address and the date it was read.
The four pages
- History of Sudoku follows the puzzle from French newspaper grids of the 1890s to the 1979 Dell publication as Number Place, Nikoli’s adoption in 1984, and the 2004 newspaper launches that made it global. It also lists the points on which the sources disagree.
- Latin squares and the math behind Sudoku explains why every Sudoku solution is a Latin square, recounts Euler’s 36 officers problem, and shows how symmetry made it possible to count every valid grid.
- How many Sudoku puzzles exist, and the 17-clue result separates the count of completed grids from the count of puzzles and explains the 2012 computer search that proved no puzzle has fewer than 17 clues.
- Sudoku variants through history surveys the sizes, regions, extra rules and arithmetic versions that appeared after 2004, and says plainly where no dated source was found.
Which page answers which question?
| Question | Page |
|---|---|
| Who invented Sudoku, and when? | History of Sudoku |
| Where does the name come from? | History of Sudoku |
| What is a Latin square? | Latin squares and the math |
| How many valid grids exist? | Latin squares and the math and the counting page |
| What is the fewest clues a puzzle can have? | The 17-clue result |
| Who created killer Sudoku? | Variants through history |
How is the history section written?
- Sources first. A fact goes in only if a source that was actually opened supports it. A page that cites a reference it did not open says that.
- Disagreements are shown. When two sources give different years or credit different people, both are stated.
- Numbers are separated by meaning. The page keeps counts of grids, grids up to symmetry and puzzles apart, since they answer different questions.
- Some arithmetic is the author’s own. Where a page does a calculation to check a published figure, it labels it as such.
- Nothing about this site is dressed up as history. Where this site’s methods differ from the historical ones, as with symmetric clue layouts, the pages say so.
The sources are mostly encyclopedia-level summaries and a small number of academic and news pages. Primary documents, such as the original Dell magazines or the journal version of the 17-clue paper, were not available to read, so the pages point to them as the place to check. If you find an error or a better source, the contact page says how to tell us.
How does this connect to the game?
The mathematics is not just background. The symmetries that define “essentially different” grids are the moves the game uses to vary stored puzzles, and the uniqueness property that the 17-clue search had to test is checked for every puzzle on the site, as explained in how puzzles are generated and verified unique. The way difficulty is graded is covered in how Sudoku difficulty is graded.
When you want to play, choose a level on the home page, or look at the games hub for the other boards. The guides hub has tutorials for learning to solve.