Killer sudoku keeps the rules of classic sudoku and adds one layer: the grid is divided into cages, groups of cells that carry a sum. The sum is written in the corner of each cage. The digits inside a cage must add up to that sum, and no digit can repeat within one cage. Some cells start with a digit already placed, but most of the work comes from the cages.

The result is a puzzle that reads differently from classic. Instead of looking only at what is on the grid, you reason about which numbers can make a given total, and that reasoning feeds into the usual row, column and box rules.

The origin of killer sudoku is less clear than the origin of classic sudoku, and the sources do not agree on a single inventor. What is well documented is that the format became popular in puzzle books and magazines in the 2000s, after classic sudoku had already spread around the world.

The idea behind it is older than the format. Puzzles that combine sums with digit rules have been around for a long time, and killer sudoku brings that idea into the grid. It is a good example of how a familiar game can be reshaped by adding one new rule.

Each cage is a set of cells with a sum, and the digits in it are different. That gives you a short list of possibilities for every cage, and the size of the cage and its sum decide how long the list is.

• A one-cell cage gives its digit at once. A cage with the sum 7 in one cell is a 7.
• A two-cell cage with the sum 3 can only hold 1 and 2, in either order.
• A two-cell cage with the sum 4 can only hold 1 and 3.
• A three-cell cage with the sum 6 can only hold 1, 2 and 3, so the cage is solved in its digits even before you place anything.
• Large sums such as 16 or 17 in two cells are also short: 16 is 7 and 9, and 17 is 8 and 9.

When you know the possibilities for a cage, the cells inside it become much easier to fill.

Every row, every column and every box contains the digits 1 to 9 exactly once, so each of them adds up to 45. This gives you a powerful shortcut. If a cage covers the rest of a row, column or box apart from a few cells, its sum tells you the total of those cells. Subtract the sums you know, and the remainder is the total of what is left.

Suppose a row has one cage of three cells with the sum 20, and the other six cells are already filled with known digits. You do not need to try every combination. The remaining cells must add up to the difference, and that narrows the choice quickly.

Killer puzzles also have starting digits, but usually fewer than classic puzzles of the same level. On the hardest levels there are very few, and the cages carry almost the whole puzzle. That is why a beginner can find killer puzzles frustrating at first and then enjoy them more than classic once the cage logic clicks.

Killer mode has five levels, named Easy, Medium, Hard, Expert and Master, like the classic levels. Each one changes how much the cages do. On Easy you can often read a cage's digits straight off its sum. On Master you combine several cages, look for cells shared between them, and use the rule of 45 across whole rows and boxes.

Start on Easy until you can name the digit options for two-cell cages without thinking. Moving up is a matter of speed as much as of new ideas.

• Start with the smallest cages. One-cell and two-cell cages give you the most information for the least work.
• Look at cages that overlap a box. If a cage lies entirely inside one box, its digits cannot appear in the rest of that box. Check the other cells of the box for those digits.
• Use the complement. When a cage and its surrounding cells cover a whole row or box, the rule of 45 gives you the sum of the cells outside the cage.
• Keep candidate lists short. Write only the digits that a cage allows. A long list is a sign that you have not used the sum yet.

Most solvers combine these as they go. No single technique solves a hard puzzle on its own.

Points in killer mode follow the same logic as classic: each correct digit scores, streaks and speed add to the total, and a completed puzzle earns a bonus. Each cage you complete also adds a small bonus of its own, which rewards the cage reasoning that makes killer sudoku what it is. Mistakes and hints cost points, as in classic.

The Rules page lists the figures and explains when a game counts toward the rankings. The rule is the same as in classic: more than three mistakes or three hints keeps the game going but takes it out of the rankings.

Killer sudoku asks for something classic sudoku asks for, and a little more: holding several constraints in mind at once, and checking whether a total can be reached in more than one way. Those are useful habits, and practising them is satisfying.

There is no solid evidence that killer puzzles, or any single puzzle type, prevent memory loss or dementia. Research on cognitive training has produced mixed results. Treat a daily puzzle as a pleasant routine and a way to focus, not as medical advice. If memory or concentration is a concern, a doctor is the right person to ask.

• Forgetting that digits do not repeat in a cage. A three-cell cage with the sum 9 cannot be 3, 3, 3.
• Writing every combination. Use only the combinations that the rest of the grid allows.
• Ignoring the rule of 45. It often finishes a row or box faster than cell-by-cell checking.
• Working on one cage for too long. If a cage will not resolve, look at the cages around it. Information usually comes from the neighbours.

Begin with one-cell and two-cell cages, then apply the rule of 45 to the rows and boxes they touch. The guide Killer Sudoku for Beginners walks through this with worked examples, and the article on mistakes beginners make covers habits that help in both modes.

If you prefer paper, the printable page offers classic puzzles, and the paper or screen guide compares the two formats.