How to play Killer Sudoku

Killer Sudoku mixes Sudoku with a little arithmetic. The grid is the classic one - nine rows, nine columns and nine 3x3 boxes that must each hold the digits 1 to 9 exactly once - and only part of it starts filled in. The grid is also divided into cages: small groups of cells outlined with a dashed line, each with a sum in its corner. The digits in a cage must add up to that sum, and no digit may appear twice in the same cage.

Every puzzle here is made fresh by the game when you start it, cages and sums included. Each has exactly one solution and can be solved by reasoning alone, with no guessing. The four levels differ in which solving techniques a puzzle demands, from simple cage combinations on Easy to large innie and outie sets 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. Thick dark lines mark the 3x3 boxes. Each cage is outlined by a dashed line running just inside its edge, and its sum is printed in small bold digits in the top-left corner of the cage. The digits you enter appear in blue.
• Choosing a cell: tap any cell. Its row, column, box and cage are shaded, 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. In the corner cell of a cage the notes move down a little, so they never cover the cage's sum. 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 cage.
• 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 cages, digits, 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. Every row, every column and every 3x3 box must end up holding each digit from 1 to 9 exactly once, just as in classic Sudoku.

Cages. Every cell belongs to exactly one cage. A cage is a group of two to six cells joined side by side. Its digits must add up to the sum shown in its corner, and they must all be different - even when the cage spreads over two boxes or bends round a corner.

Givens. Some digits are placed at the start (more on the easier levels) and can't be changed. Together with the cages and their sums they fix the solution, and every puzzle has exactly one.

Mistakes - Unlimited (the default). A digit that is already in the same row, column, box or cage is marked in red and the mistakes counter goes up by one. So is a digit that breaks its cage's sum: a full cage whose digits don't add up to the sum, or a cage whose digits already leave no possible total for its empty cells (for example a 1 in a two-cell cage of 17). Nothing else is checked: a digit that breaks no rule you can see 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 is marked. Because the solution is unique, such a grid 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.

• Cage combinations: some sums can only be made one way. Two cells adding up to 3 must be 1 and 2; two cells making 17 must be 8 and 9; three cells making 6 must be 1, 2 and 3; three cells making 24 must be 7, 8 and 9. Other sums have a few combinations, and any digit that appears in none of them can be crossed out. A digit that every combination needs, with only one place left in the cage, goes there.
• Singles: a digit that can only go in one cell of a row, column or box, and a cell where only one digit is still possible - the classic Sudoku scans, which work alongside the cages from the first move.
• The 45 rule: the digits 1 to 9 add up to 45, so every row, column and box totals 45. Add up the cages lying wholly inside a box; if one cell of the box belongs to a cage that pokes out, that cell (an "innie") is 45 minus that total. In the same way, a cell sticking out of a box from a cage that is otherwise inside (an "outie") is the cage total minus what the box still needs.
• The 45 rule over several houses: two or three rows, columns or boxes together total 90 or 135, which pins down single innies and outies across a whole band.
• Cage permutations: check that a combination can really be placed - 8 and 9 in two cells where only one cell can take a 9 fixes both.
• Cage and house interactions: if a digit every combination of a cage needs can only sit in one row, column or box of that cage, it can't go anywhere else in that house. And if a house's only places for a digit are all inside one cage, the cage's other cells can't hold it.
• Pointing, box-line reduction and pairs: the classic Sudoku eliminations, as on Normal Sudoku.
• Innie and outie sets: when two or three cells are left over by the 45 rule, their total is known even if each digit isn't, and only the combinations that make it survive.
• Advanced: larger innie and outie sets of four or five cells, triples, X-Wings, XY-Wings and, now and then, longer chains - all still without guessing.

Strategy tips

• Start with the extreme cages. Look for the sums that can only be made one way: small sums in small cages and large sums in small cages. They give you the first certain digits.
• Use the 45 rule early and often. In almost every Killer Sudoku the first real breakthrough comes from adding up the cages in a box, a row or a column. Look for houses where only one cell sticks in or out.
• Combine cages with the grid. A cage of 3 in two cells holds 1 and 2; if it sits inside one row, no other cell of that row can hold a 1 or a 2.
• Write combinations as notes. For a cage with only a couple of possible combinations, pencil in the digits they share and the ones they don't - the notes move out of the way of the cage's sum.
• Watch the red. In the default mode a cage turns red as soon as its digits can no longer reach the sum, so an arithmetic slip shows up right away.
• Don't guess. Every puzzle here can be solved by logic. If you feel stuck, add up another house - the 45 rule usually holds the next step.

Difficulty levels

The game generates every puzzle on the spot, cutting a freshly filled grid into cages and reworking them until its solver - which works the way a person does, always taking the easiest step available - can finish the empty grid at the level you chose. Then part of the solution is filled in for you - the more, the easier the level - which often makes the hardest step unnecessary, so the levels differ mostly in cage size and in how much of the board you start with.

• Easy: at least half the board is filled in (41 of 81 cells); mostly cages of two and three cells; cage combinations, singles and the 45 rule inside one row, column or box are all you need.
• Normal: at least 40% of the board is filled in (32 of 81 cells); cages of two to five cells; a step can need the 45 rule across several houses, a cage permutation, a cage-house interaction, a pointing pair or a pair.
• Hard: at least 30% of the board is filled in (24 of 81 cells); bigger cages; a step can need an innie or outie set of two or three cells, a triple, an X-Wing or an XY-Wing.
• Crazy: at least 20% of the board is filled in (16 of 81 cells); the biggest cages, up to six cells; a step can need a large innie or outie set, a quad, simple colouring or a chain.

Statistics and best times are kept separately for each level. If you are new to Killer Sudoku, start on Easy and learn the common two- and three-cell combinations before moving up.