Sudoku Solver, Step by Step

A sudoku solver that shows its working

Type the numbers you have into the grid, using the arrow keys to move around. Explain the next move finds the next square that can be filled with certainty, highlights the row, column or box that proves it, and says why in plain words. Keep pressing to walk through the whole puzzle, or step back to look again. When a move removes possibilities rather than filling a square, the small pencil marks show which digits go.

Show the answer fills the grid at once and says whether the answer is the only one. A fair sudoku has exactly one, so if it reports several, a number is missing from what you typed.

The techniques, in plain words

Only one digit fits. Every other digit is already in the square's row, column or box, so only one is left. Only one place for a digit. A row, column or box still needs a digit and only one of its squares can take it. These two solve most puzzles in a newspaper.

Pointing and claiming: when a box's last few places for a digit all lie in one row or column, that digit is spoken for and can be crossed off the rest of that line, and the other way round. A pair: two squares in a line that can only be the same two digits take both of them between them, so no other square there can be either. A hidden pair is the reverse, two digits with only two places to go. X-wing: if a digit has only two places in each of two rows, and they line up in the same two columns, it must take one place in each column, and can be crossed off everywhere else in them.

For killer sudoku there are two more. Cage combinations: a cage's digits never repeat and must add up to its sum, so a cage of 17 in two squares can only be 8 and 9, and anything else is crossed off. The 45 rule: every row, column and box holds 1 to 9, which add up to 45. Subtract the cages lying wholly inside it, and whatever is left over has a known total; when only one square is left over, that square is solved outright.

Some puzzles need more than these. When the explanation runs out of certain moves it says so rather than guessing, and Show the answer finishes it.

Variant sudoku: X, windoku, anti-knight and miracle

Tick a rule and the solver uses it, both for the answer and in its explanations. Each one has a new puzzle every day on its own page: X sudoku, with both diagonals, windoku, with four shaded windows, disjoint groups, centre dot, anti-knight, anti-king, anti-knight-king, non-consecutive, and miracle sudoku, which uses three of these rules at once and can start from as few as five givens. The rest of the daily puzzle games include thermo, arrow and fourteen more.

Thermo, arrow and other line sudoku

Pick a kind of line, press Draw lines and drag along each line in the puzzle; tap a line to remove it. The solver uses the line's rule for the answer and in every explanation, alongside the usual rows, columns and boxes. On a thermometer the digits rise from the bulb. An arrow's digits add up to the digit in its circle. Neighbours on a German whispers line differ by at least 5, so 5 never sits on one. A renban line holds a run of consecutive digits in any order. A palindrome reads the same from either end, and a between line holds digits strictly between those in the circles at its ends. Each has a daily puzzle: thermo, arrow, German whispers, renban, palindrome and between lines.

Sandwich, skyscraper and little killer sudoku

These puzzles put their clues outside the grid. Choose the kind under Clues outside the grid and the boxes round the grid open. A sandwich clue is the sum of the digits between the 1 and the 9 in that row or column; 0 means the 1 and 9 sit side by side. A skyscraper clue counts the digits you can see from that side if each digit is a tower of that height, with taller ones hiding shorter ones behind them. A little killer clue, with its small arrow, is the sum of the diagonal it points along, where digits may repeat. Each has a daily puzzle: sandwich, skyscrapers and little killer.

Kropki, XV and greater-than sudoku

These puzzles put marks on the line between two squares. A white dot joins two consecutive digits and a black dot two where one is double the other. An X joins two that add up to 10 and a V two that add up to 5. A greater-than sign points at the smaller of the two. When every dot is shown, two squares with no dot between them are neither consecutive nor double, and the same goes for X and V; tick the box when the puzzle says so, as most do. Each has a daily puzzle: kropki, XV and greater-than.

Even-odd, quadruple and clone sudoku

Choose a mark, press Mark squares and tap the squares it belongs to. A grey square holds an even digit and a grey circle an odd one. A quadruple is a small circle where four squares meet, listing digits that must appear among those four: type the digits, then tap the top-left square of the four. Clone regions are two shaded areas of the same shape whose matching squares hold the same digits: drag across one, then the other. Each has a daily puzzle: even-odd, quadruple and clone regions.

Jigsaw sudoku solver

In a jigsaw sudoku the nine 3 by 3 boxes are replaced by nine irregular regions of nine squares, and each region holds 1 to 9 just as a box would. Tick Irregular regions, press Paint the regions, pick a colour and drag across each region's squares; the heavy lines follow the regions as you paint. The solver checks each region has exactly nine squares, then explains or solves the puzzle with the same moves as a classic one, pointing and claiming included. The daily jigsaw sudoku has a new one every day.

Killer sudoku solver and cage calculator

Press Draw cages, then tap or drag across the squares of a cage, type its sum and press Make cage. Repeat for each cage; tap one to select it again if you need to change it. The page keeps a running total: when the cages cover the whole grid their sums must come to exactly 405, so a typo shows up straight away. Type any given digits into the grid as usual, then explain or solve it like any other sudoku. The daily killer sudoku has a new one every day.

The cage calculator below is the killer cheat sheet: give it a number of squares and a sum and it lists every set of different digits that makes it. Leave out digits a cage cannot use, or require one it must, and the list narrows.

How it was checked

Before this page went up, the solver was run on 135 puzzles from nine of the site's daily variant pages. It found each page's own stored answer every time, and found it to be the only one, which also proves each variant's rule is set up right. Every step the explanation took was checked against those answers: it never placed a wrong digit and never crossed off a right one. 131 of the 135 were solved start to finish by explained moves alone.

Killer sudoku was checked the same way against all 200 puzzles from the daily killer page: every stored answer found, every one the only answer, every explained step true, and all 200 explained from start to finish.

More puzzles like this

If you like a puzzle that yields to patience rather than luck, that is exactly what a good interlocking puzzle asks of you. See the 6 Piece Cross, or the rest of the brain teasers. There are more solvers on the puzzle tools page.