Printable sudoku

A sudoku is a 9 × 9 grid split into nine 3 × 3 boxes, with some numbers already filled in. Fill every empty square so that each row, each column and each box holds the numbers 1 to 9, each once. There's no adding up: the numbers are only symbols, and letters or pictures would work the same way.

Every puzzle on this page has exactly one answer. That's checked by a program that tries every way of finishing the grid and stops if it finds a second one. So each square can be worked out from the others, and you never need to guess.

The small grids follow the same rule. A 4 × 4 grid has four 2 × 2 boxes and uses 1 to 4. A 6 × 6 grid has six boxes, each two rows high and three columns wide, and uses 1 to 6. They're a good start for children, and the easy ones need nothing more than the first two techniques below.

Each puzzle starts as a complete, valid grid filled in a random order. Numbers are then taken out in pairs, each square with its partner turned half round the centre, which gives the symmetrical pattern printed sudoku usually has. After each removal the program checks that only one answer remains, and puts the pair back if not.

Then a second program solves the puzzle the way a person would, using the techniques above, always the simplest one that makes progress. The grade is the hardest technique it needed. Easy puzzles need only singles and keep 36 of the 81 numbers. Medium puzzles need pointing or claiming, or singles with 30 or fewer numbers given. Hard puzzles need a pair or triple. Expert puzzles need an X-Wing, Swordfish or XY-Wing. A puzzle that needs anything beyond that is thrown away, so every sheet can be solved by logic alone. The 4 × 4 and 6 × 6 grids come in easy and medium.

The sheet number is the seed for the random choices, so the same settings and number always give the same puzzles. Write it down, or read it off the foot of a printed page, and you can print the same sheet again later. The technique names follow HoDoKu's guide to solving techniques, linked under Sources.

The modern puzzle first appeared in 1979 in Dell Magazines in the United States, under the name Number Place, and was most likely devised by Howard Garns, a retired architect. The Japanese publisher Nikoli took it up in 1984 under a name meaning "the digits must be single", later shortened to sudoku.

The fewest givens a 9 × 9 sudoku can have and still have only one answer is 17. Gary McGuire, Bastian Tugemann and Gilles Civario showed by an exhaustive computer search, published in 2014, that no 16-clue puzzle exists.