How to play Sudoku X

Sudoku X, also called diagonal Sudoku, is classic Sudoku with one extra rule: the two long diagonals of the grid, corner to corner, must also contain the digits 1 to 9 exactly once. That single rule changes how the puzzle plays. The centre cell sits on both diagonals, every box along them gains new neighbours, and a digit you place in a corner now reaches across the whole board.

Every puzzle here is made fresh by the game when you start it, has exactly one solution, and can be solved by reasoning alone. You never need to guess. The four levels differ in which solving techniques a puzzle demands, from simple scanning on Easy to chains and wings on Crazy.

How to play on skill.games

When you open the game, the settings popup appears. Choose a level under DIFFICULTY, choose how mistakes are treated under MISTAKES, and press PLAY. A new puzzle is generated in a moment.

• The board takes up most of the screen. The cells of the two diagonals are shaded grey with fine stripes, so you can follow them even on a small phone; a faint line runs through the diagonal cells that are still empty. The digits printed in dark ink are the givens; they can't be changed. The digits you enter appear in blue.
• Choosing a cell: tap any cell. Its row, column and box are shaded - and its diagonal too, if it lies on one - and every cell holding the same digit is highlighted.
• Entering a digit: with a cell chosen, tap a number on the number pad (under the board, or beside it when your screen is wider than it is tall). The small number under each key shows how many of that digit are still to place; a key fades out once all nine are on the board.
• NOTES: tap NOTES to switch notes on. Numbers you tap are now pencilled into the cell in small print as candidates, and tapping one again removes it. Tap NOTES again to go back to entering digits. When you enter a digit, it is removed automatically from the notes of every cell in its row, column, box and diagonal.
• ERASE clears the chosen cell (its digit or its notes).
• UNDO takes back your last action - a digit, a note or an erase - all the way back to the start. Undo is free and unlimited.
• Highlighting a digit: with no cell chosen, tap a number on the pad to highlight every cell and note holding that digit. Tap it again to clear the highlight.

On a computer you can also use the keyboard: the arrow keys (or W, A, S, D) move between cells, 1 to 9 enter a digit, Shift and a digit pencil a note, Backspace, Delete or 0 erase, N switches notes on and off, and Z undoes.

The top line shows the clock, the level and your mistakes. The clock runs only while you play: it stops when the menu or a popup is open. The menu button in the top-left corner pauses the game, starts a new puzzle or switches the sound on or off. The game is saved after every move, so if you close the page you can press CONTINUE later and carry on with the same grid, notes, clock and undo history.

When the last cell is filled correctly, the board ripples and the results screen shows your time, your best time at that level (a star marks a new record), your mistakes and the puzzle's code, together with your wins, losses, win rate and streaks.

Rules

The grid. The board has 9 rows, 9 columns and 9 boxes of 3x3 cells, plus two diagonals of 9 cells each: from the top-left corner to the bottom-right, and from the top-right to the bottom-left. Every row, column, box and both diagonals must end up holding each digit from 1 to 9 exactly once.

Givens. The puzzle starts with some digits already placed. They are part of the puzzle and can't be changed. Every puzzle has exactly one way to complete it.

Mistakes - Unlimited (the default). If you enter a digit that is already in the same row, column, box or diagonal, the clash is marked in red and the mistakes counter goes up by one. Nothing else is checked: a digit that doesn't clash with anything is not marked, even if it turns out to be wrong later - just as on paper. The puzzle is solved when every cell is filled and nothing clashes. Because the solution is unique, a full grid without clashes is always the right one.

Mistakes - 3 lives. Every digit you enter is checked against the solution at once. A wrong digit is marked in red and costs a life; the third mistake ends the game and counts as a loss. Undo can take a wrong digit back, but not the life it cost.

Abandoned puzzles. Starting a new puzzle before finishing the current one counts as a loss in your statistics for that level.

Solving techniques

These are the methods the game's own solver uses to grade every puzzle, from the simplest up. In Sudoku X each one works on the diagonals exactly as it does on rows, columns and boxes.

• Hidden single: a digit that can only go in one cell of a row, column, box or diagonal. Scan the diagonals as well as the boxes - they are often the quickest way in.
• Naked single: a cell where only one digit is still possible. Cells on a diagonal see more of the board, so they run out of options sooner; the centre cell sees the most of all.
• Pointing and line-box reduction: if a digit's only places in a box lie on one row, column or diagonal, it can't go anywhere else on that line - and if a line's only places for a digit lie in one box, it can't go anywhere else in that box. The diagonals add new intersections of this kind.
• Naked and hidden pairs: two cells in a unit that can only hold the same two digits claim those digits; two digits that can only go in the same two cells claim those cells.
• Triples and the X-Wing: the same idea with three cells or digits; and a digit confined to the same two columns in two rows can be removed from the rest of those columns.
• XY-Wing: three two-candidate cells linked so that one digit must sit in one of the two outer cells - any cell seeing both can't hold it. With the diagonals, more cells see each other, so wings reach further.
• Advanced: XYZ-Wing, Swordfish, quads, simple colouring and XY-Chains - longer chains of "if this, then that" reasoning, all still without guessing.

Strategy tips

• Start with the diagonals. They cross every box on the way, so a digit missing from a diagonal is often easy to pin down.
• Watch the centre. The middle cell belongs to its row, its column, its box and both diagonals - five units at once. Once it is filled, a lot falls into place.
• Corners matter too. Each corner cell sits on a diagonal, so a corner digit rules out its number along the whole diagonal.
• Use notes once singles run out. Pencil in the candidates of a box or a diagonal, then look for pairs and pointing digits among them.
• Watch the number pad. A key that shows 1 means a single copy of that digit is still missing - often easy to find.
• Don't guess. Every puzzle here can be solved by logic. If you feel stuck, look along the diagonals for a pattern you haven't spotted yet.

Difficulty levels

The game generates every puzzle on the spot and grades it with a solver that works the way a person does, always using the easiest step available. A puzzle is given to you only if its hardest required step matches the level you chose. The diagonals add information, so Sudoku X puzzles start with fewer givens than classic Sudoku at the same level.

• Easy: at least half the board is filled in (41 of 81 cells); scanning for hidden and naked singles is all you need.
• Normal: at least 40% of the board is filled in (32 of 81 cells); at least one step needs a pointing pair, a line-box reduction or a naked or hidden pair.
• Hard: at least 30% of the board is filled in (24 of 81 cells); at least one step needs a triple, an X-Wing or an XY-Wing.
• Crazy: at least 20% of the board is filled in (16 of 81 cells); at least one step needs simple colouring, an XY-Chain, an XYZ-Wing, a Swordfish or a quad.

Statistics and best times are kept separately for each level. If you are new to Sudoku X, start on Easy and get used to scanning the diagonals before moving up.