Where Sudoku Comes From, and How a Puzzle Is Made

Games & Puzzles ·

Sudoku has a Japanese name, but it was invented in America, named in Japan, and made famous by a New Zealander in London. Here’s how a nine-by-nine grid of numbers took over the world, and how a puzzle like the ones on this site is actually made.

Want to play? Try today’s Sudoku, or print a stack of printable Sudoku puzzles with an answer key.

The rules in one sentence

Fill the grid so that every row, every column and every 3×3 box contains each of the numbers 1 to 9 exactly once. Some numbers are given; the rest you work out by logic.

The numbers don’t really matter. You could play with nine letters, colors or symbols, because there’s no arithmetic involved, only placement.

Before Sudoku: Latin squares

In the 1780s the Swiss mathematician Leonhard Euler studied what he called Latin squares: grids where each symbol appears once in every row and every column. A finished Sudoku is a Latin square with one extra rule, the 3×3 boxes.

In the 1890s, French newspapers such as Le Siècle and La France printed number puzzles that came very close to Sudoku, based on magic squares. They faded away by the First World War.

Number Place: the American invention

The puzzle we know first appeared in 1979 in Dell Pencil Puzzles and Word Games, a US puzzle magazine, under the name Number Place. It was almost certainly created by Howard Garns, a retired architect from Indiana, then in his seventies. Garns died in 1989, before his puzzle became famous, and he never got credit in his lifetime.

Sudoku: the Japanese name

In 1984 the Japanese puzzle publisher Nikoli introduced Number Place to Japan. Its president, Maki Kaji, gave it a name that translates roughly as “the digits must be single”, shortened to sudoku: su (number) and doku (single).

Nikoli added two conventions that stuck: the starting numbers are laid out in a symmetrical pattern, and every puzzle should be solvable by logic alone. Sudoku became a hit in Japan, while in America it stayed a minor magazine puzzle.

The 2005 craze

In 1997 Wayne Gould, a retired judge from New Zealand living in Hong Kong, came across a Sudoku book in a Tokyo bookshop. He spent six years writing a computer program to generate puzzles, and offered them to newspapers. The Times in London printed its first one on 12 November 2004. Other British papers rushed to copy it, and within a year Sudoku was in newspapers around the world, along with books, TV shows and championships.

Some numbers about the numbers

  • There are 6,670,903,752,021,072,936,960 valid completed Sudoku grids, as calculated by Bertram Felgenhauer and Frazer Jarvis in 2005. If you count grids that are just rotations, reflections or relabelings of each other as the same, there are still about 5.5 billion different ones.
  • The fewest starting numbers a puzzle can have and still have exactly one solution is 17. That was proved in 2012 by Gary McGuire and colleagues, after an exhaustive computer search showed no 16-clue puzzle exists.
  • The number of clues doesn’t decide how hard a puzzle is. Some 17-clue puzzles are easy, and some with 30 are fiendish.

How a Sudoku puzzle is made

The puzzles on this site are made by a computer in your browser, a new one each time. The method is the classic one:

  1. Fill a complete grid. Start with an empty grid and fill it in at random, backing up whenever a number won’t fit. The result is a finished, valid Sudoku: the answer.
  2. Take numbers away. Remove numbers one pair at a time. Each pair is a square and its mirror image through the center, which is what gives the clues their symmetrical pattern.
  3. Check after every removal. After each pair, a solver counts how many solutions the puzzle now has. If it’s still exactly one, the numbers stay out. If removing them would allow a second solution, they go back.
  4. Stop at the right difficulty. Keep going until the puzzle has about as few clues as its level aims for, while still being solvable with that level’s techniques.

The uniqueness check is what separates a good Sudoku from a bad one. If a puzzle has two solutions, at some point you’d be forced to guess, and the logic falls apart.

How difficulty is graded

Difficulty comes from which techniques you need, not from how many numbers are missing. The grader tries to solve each puzzle the way a person would, using only certain techniques:

  • Naked single: a square where only one number is possible, because the other eight already appear in its row, column or box. Spotting these is all an easy puzzle needs.
  • Hidden single: a number that can only go in one square of a row, column or box, even though that square could hold other numbers too. A medium puzzle needs these as well, and can’t be finished with naked singles alone.
  • Beyond singles: a hard puzzle can’t be finished with singles at all. You’ll need to pencil in notes and look for patterns in them, such as two squares in a row that can only be 4 or 7, which means no other square in that row can be 4 or 7.

As a rough guide, easy puzzles here start with about 38 numbers, medium about 30 and hard about 24, but the techniques are what really sets the level.

Tips for getting better

  • Scan by number. Pick a number, say 5, and check each box: where could the 5 go? This finds hidden singles quickly.
  • Use notes on harder puzzles. Writing the possible numbers in each square turns a hard puzzle into a pattern-spotting one.
  • Never guess. Every puzzle here has exactly one solution, so there’s always a logical next step, even if it’s hard to see.

Ready? Play today’s puzzle: everyone gets the same easy, medium and hard puzzle each day.