Sudoku

How to play

Sudoku, also called number place, is a puzzle made of numbers. The grid has 81 squares, in nine rows and nine columns, and thicker lines divide it into nine boxes of three squares by three. Some squares already hold a number. Your job is to fill every empty square with a number from 1 to 9, so that each row, each column and each box holds every one of the numbers 1 to 9 exactly once. You never add anything up. The numbers are only labels, and every square can be worked out by looking at the numbers around it.

1. Choose a square. Tap or click an empty square. It gets a heavy outline, its row, column and box are shaded, and any square with the same number is highlighted. The line under the grid names the chosen square. Numbers that came with the puzzle are bold on a grey square, and they cannot be changed.
2. Tap a number. Tap one of the number buttons under the grid to write that number in the chosen square. Tap the same number again to take it out. With a keyboard, move around the grid with the arrow keys and press 1 to 9 to write a number. Press 0, Backspace or Delete to empty a square.
3. Watch for repeats. If a number appears twice in a row, column or box, both are underlined and the page says so. A number button shows a tick once all nine of that number are on the grid.
4. Finish. When every square has a number and no row, column or box repeats one, the page tells you that you solved it.

If you like to jot reminders, press Make a note above the number buttons. The buttons then add small notes to the chosen square instead of writing an answer. A square with notes shows a small mark in its top right corner. While Make a note is chosen, the number buttons for the chosen square's notes show as ticked, and the line under the grid lists them in any case. Notes never count as part of your answer. Erase removes a square's number or, if it has none, its notes. The notes are shown outside the squares because numbers small enough to fit inside would be too small to read comfortably.

There is no timer and no score, and the page never moves on to another puzzle by itself. To start again, press Clear board under the grid. It empties everything you added and hides the answers. If you pressed it by mistake, press the same button, which now says Undo clear, before you change anything else.

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Worked example

Here is the start of an Easy puzzle, solved a few steps at a time. Each picture shows the grid after that step, and no guessing is needed.

In each picture, the squares being looked at are shaded, the numbers that matter most are dark like 6, and the new number has an orange frame around it. Numbers written in earlier steps are blue.

1. 	4	1		6	5			7
   2	9		3			5
   8				2		4		9
   7			4	5	6	1
   		2	1		3	7
   		4	8	7	2			6
   1		6		8				3
   		3			9		5	8
   9			5	3			1

   Only one number fits. Look at the shaded square in row 1, column 3. Its row already holds 4, 5, 6 and 7. Its column adds 2 and 3, and its box adds 8 and 9. That is eight different numbers: 2, 3, 4, 5, 6, 7, 8 and 9. Only 1 is missing, so 1 goes in this square. Tap the square, then tap the 1 button.

2. 	4	1		6	5			7
   2	9		3			5
   8	6			2		4		9
   7			4	5	6	1
   		2	1		3	7
   		4	8	7	2			6
   1		6		8				3
   		3			9		5	8
   9			5	3			1

   Only one place fits. Now look at the top left box and ask where its 6 can go. There is already a 6 in the top row and a 6 in the third column (they are dark in the picture), so no square of the box in that row or that column can hold a 6. That rules out the top left square, which is in the top row, and the squares in rows 2 and 3 of the third column. The only empty square left in the box is row 3, column 2, so write 6 there.

3. 	4	1		6	5			7
   2	9		3			5
   8	6			2		4	3	9
   7			4	5	6	1
   		2	1		3	7
   		4	8	7	2			6
   1		6		8				3
   		3			9		5	8
   9			5	3			1

   One answer leads to the next. The new 6 helps elsewhere. Look at the shaded square in row 3, column 8. Its row holds 2, 4, 6, 8 and 9, its column adds 1 and 5, and its box adds 7. That makes eight numbers again, and only 3 is missing. Write 3 in the square.

Carry on in the same way and the whole grid fills in. On an Easy puzzle you only ever need the first idea: a square where eight of the nine numbers are already ruled out by its row, column and box.

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Levels and the daily puzzle

Each level has its own daily puzzle, which changes at midnight where you are. When you have finished, press Next puzzle for another, as many as you like. A puzzle you have started is remembered in this browser, so you can come back to it later. Every puzzle has exactly one solution, and none needs guessing.

• Easy: one number fits. Every step is a square where only one number fits, because the other eight are already in its row, column or box. Around 38 numbers are given.
• Medium: one place fits. Sometimes no square has only one number left. Then pick a number and a row, column or box instead, and look for the one square where that number can still go, as in the second step above. You will need this as well as the first idea. Around 30 numbers are given.
• Hard: pairs and lines. Now and then neither of those ideas helps, and you need one of these. A pair: if two squares in the same row, column or box can only hold the same two numbers, say 3 and 8, then those two squares use up the 3 and the 8, so no other square in that row, column or box can be 3 or 8. The same goes if two numbers can only go in the same two squares: those squares must hold them, so they can hold nothing else. A line: if, inside one box, a number can only go along one row, then it cannot go anywhere else along that row outside the box. Likewise, if along a row a number can only go in one box, it cannot go anywhere else in that box. Around 25 numbers are given.

Each level is only used for a puzzle that really needs it: a Medium puzzle cannot be finished with the first idea alone, and a Hard puzzle cannot be finished with the first two.

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Tips

• Start with the numbers that already appear many times. If seven of the nine 4s are on the grid, there are only two places left for the others.
• Look for a row, column or box that is nearly full. With only two or three empty squares, there is very little to work out.
• Choose a square, then compare its row, column and box. The line under the grid names the square you have chosen, and the shading shows which squares to compare.
• Use notes when you are stuck, not before. Writing every possible number in every square takes a long time, and the puzzles are made to be solved without it.
• If a number is underlined, one of its twins is wrong. It is not always the one you wrote last, so check both.
• If the numbers feel small, press Text size at the top of the page.
• Stuck? Show answers fills in every square, and Print, then Print with answers, puts the finished grid on a second page.

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How these puzzles are made

Every puzzle is made by a program from the date or puzzle number, so the same day always gives the same puzzle at each level. The program first fills a whole grid with numbers that follow the rules, choosing at random from the date. Then it takes numbers away, first two at a time from opposite sides of the grid and then one at a time. After every removal, it solves the puzzle again using only the ideas that the level allows, the way a person would and never by guessing. A number is taken away only if the puzzle can still be finished that way. That is how the program knows there is exactly one solution: each idea is a step that must be true, so a puzzle that can be finished using them has no other answer. A puzzle is used at a level only if that level's ideas finish it and the level below's do not. Before a puzzle appears, the page checks it again with a separate search that counts every solution it can find. Whether you have solved it is decided by the rules, not by comparing with a stored answer. Automated tests repeat these checks on thousands of puzzles whenever the puzzle code changes, using a second checker written separately from the one that makes the puzzles.

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