Play 4×4 Sudoku Online

What is 4×4 Sudoku?

4×4 Sudoku is Sudoku shrunk to sixteen cells. The grid has four rows, four columns and four 2×2 boxes, and you fill it with the digits 1 to 4:

• each row holds 1, 2, 3 and 4 exactly once;
• each column holds 1, 2, 3 and 4 exactly once;
• each 2×2 box holds 1, 2, 3 and 4 exactly once.

It is also sold as mini Sudoku, and puzzle writers call it Shidoku, from shi, Japanese for four. The rules are the rules of classic 9×9 Sudoku; only the size changes.

Every puzzle this page deals has exactly one answer. The generator removes clues one at a time and puts a clue back whenever taking it away would allow a second solution. That is what makes the game’s red mark on a wrong digit fair: there is never another digit that would also have worked.

How do you solve a 4×4 Sudoku?

One question does all the work: which digits can this cell already see? A cell shares its row with three other cells, its column with three more, and its box with one cell that is in neither. If those neighbours already show three different digits, the fourth is the only one left and the cell is solved. That is a naked single, and on a 4×4 grid it is the whole game.

Pencilling every possibility in, as the picture does, is optional on a board this small — most people just look — but it shows the shape of a Hard puzzle clearly: twenty-two marks, and only three places where the answer is already settled.

You will often spot another way in first. In row 1 of that puzzle, the digit 1 has only one cell it can go in, R1C3, because columns 1 and 4 already hold a 1 and R1C2 is the given 3. That is a hidden single, and it is just as correct. It is a shortcut, though, never a requirement.

What happens after the first digits go in?

Each digit you write in gives its neighbours one more thing to see, so solving a 4×4 is a chain: fill the cells that are forced, look again, and new ones appear.

That is why Hard feels harder even though it asks for nothing new. With five clues there are fewer digits for each cell to see, so fewer cells are settled at a time and the chain runs longer — three rounds here, against one or two on most Easy boards.

Does a 4×4 Sudoku ever need more than naked singles?

No — and we checked every possible one. We took all 288 completed grids and every combination of clues each of them could show, 18,874,368 clue sets in all. Of those, 13,579,680 have exactly one answer, and a solver allowed nothing but naked singles finishes every single one. It never needs a hidden single, a pair, an X-Wing or a guess. A second, deliberately plain checker, which just fills any cell whose neighbours show three different digits, re-solved 324,311 of those puzzles and agreed on all of them without writing a wrong digit.

So when a 4×4 feels stuck, the answer is never a new trick. It is a cell you have not looked at yet.

How many 4×4 Sudoku puzzles are there?

There are 288 ways to fill a 4×4 grid correctly. Most of them are the same grid in disguise: swap the two top rows, swap every 1 with a 3, or flip the grid along its diagonal, and you get another of the 288. Once those moves are allowed, only two genuinely different grids are left. A family of 96 looks like 1234 / 3412 / 2143 / 4321, and the other 192 look like 1234 / 3412 / 2341 / 4123. For comparison, classic Sudoku has 6,670,903,752,021,072,936,960 completed grids.

Puzzles are a bigger count, because a puzzle is a grid with most of its digits hidden. Here is every clue set of every grid that leaves exactly one answer:

Every clue set of all 288 completed grids — 18,874,368 in all — checked for a unique solution. A puzzle is minimal when removing any one of its clues lets in a second answer. Sudopedia’s widely copied total of 13,581,312 is 1,632 higher; the count here was re-checked by brute-force solving grids from both families.

What is the fewest clues a 4×4 Sudoku can have?

Four. No three-clue puzzle has a single answer, and 25,728 four-clue puzzles do — every one of them minimal, since taking any clue away leaves three. At the other end, a minimal 4×4 never has more than six clues: every puzzle with seven or more has at least one clue it could lose and still keep one answer.

The same question for 9×9 was only settled in 2012, and the answer there is 17. Our 17-clue Sudoku page tells that story.

How do the Easy, Medium and Hard levels differ?

Each level is a clue target. The generator fills a grid, then removes clues in random order, keeping any clue whose removal would allow a second answer, until it reaches the target. We ran it 20,000 times per level:

20,000 puzzles per level from this page’s own generator, with a fixed random seed. A round fills every cell that is forced at that moment, then looks again. Easy and Medium always hit their clue target; Hard stopped at six clues on 59 of 20,000 boards, when no remaining clue could be removed without allowing a second answer.

Every level falls to naked singles, so the difference is how much you can see at once. About a quarter of Easy boards (23.9%) have all six missing cells forced from the start. On Hard, one board in thirty (3.4%) shows a single forced cell and nothing else, and nearly a third of Hard puzzles are minimal — every one of the five clues is needed.

What do the buttons do?

Tap a cell, then a digit. The rest of the controls:

• Notes switches between writing a digit and pencilling it in. When you place a correct digit, the game removes that digit from the notes in its row, column and box for you.
• Erase clears the selected cell. Tapping the digit that is already in a cell clears it too.
• Undo steps back one change to one cell. It does not put back notes that a placement cleared elsewhere, and it does not take a mistake off the counter.
• Hint writes the correct digit into one cell that is still empty or wrong.
• Solve asks for confirmation, then fills in the whole answer.
• New Game deals a fresh puzzle at the current level, and the Easy, Medium and Hard buttons deal one at that level.

A wrong digit turns red as soon as you enter it and adds one to the Mistakes counter, so errors never wait until the end to surface. A timer runs from the moment the puzzle is dealt. On a keyboard, 1–4 enter digits, the arrow keys move, Backspace or Delete erases and Ctrl+Z undoes. Your puzzle is saved in the browser as you go, so closing the tab and coming back resumes it, timer included — though the undo history starts fresh.

4×4, 6×6 or 9×9: what to play next

The step up is gentle if you take it in order:

Level names are the buttons on each game page. The 6×6 boxes are oblong: two rows tall and three columns wide.

6×6 Sudoku is the natural next step. With six digits, a cell has to see five different digits before it is settled rather than three, and the oblong boxes take a little getting used to. After that comes classic Sudoku, starting at Easy.

Teaching a child? Our Sudoku for Kids page compares the three starting grids and covers teaching Sudoku at home and in class. You can also make your own 4×4, 6×6 or 9×9 sheets with the Sudoku generator.

Printable 4×4 Sudoku

To solve on paper, there are three free PDFs, one per level, each with 100 puzzles and the answers at the back: Easy, Medium and Hard. The printable 4×4 Sudoku page describes all three, and the full printable Sudoku collection covers the other sizes and levels.