Killer Sudoku

Sudoku with a twist of arithmetic. All the usual rules apply, but the grid is carved into dashed cages, and the numbers in each cage must add up to a small total, with no digit repeated inside a cage.

The idea behind Killer Sudoku

Killer Sudoku is what you get when you cross a Sudoku grid with a simple sums puzzle. The famous three rules are still in force, but the starting numbers are usually gone. In their place, the board is divided into outlined groups of cells called cages, each printed with a target total. Your clues are no longer "this cell is a 7"; they are "these three cells add up to 15". That shift makes the puzzle feel like detective work, where a little arithmetic and a lot of logic slowly narrow the possibilities until the grid gives itself away.

The rules

• Every row, column and 3×3 box contains 1 to 9 exactly once, just like classic Sudoku.
• Every cage, marked by the dashed outlines, adds up to the small number printed in its corner.
• A digit may not repeat inside a cage, even where the row, column and box would otherwise allow it.

Most boards begin with no given numbers at all, so the cage totals carry the whole puzzle. Every one still has a single, guess-free solution.

How to crack it: the core logic

The fastest progress comes from cages whose sums leave no choice. A two-cell cage totalling 3 can only be 1 and 2. A two-cell cage totalling 17 can only be 8 and 9. A three-cell cage summing to 6 must be 1, 2 and 3. Learning these cage combinations turns many cages into near-certainties before you place a single number.

The second tool is the rule of 45. Every row, column and box contains the digits 1 through 9, which always add up to 45. If a group of cages fills a box except for one stray cell, you can subtract the cage totals from 45 to find that cell exactly. This trick, often called innies and outies, applied to rows, columns and boxes, unlocks positions that pure Sudoku logic cannot see.

From there the ordinary techniques take over. Pencil notes let you track the surviving candidates, and each number you place tightens both its unit and its cage.

A handful of cage combinations worth knowing

Because a cage cannot repeat a digit, small cages with extreme totals often have just one possible set of numbers. These are the footholds every solver leans on:

• Two cells: 3 is {1,2}; 4 is {1,3}; 16 is {7,9}; 17 is {8,9}.
• Three cells: 6 is {1,2,3}; 7 is {1,2,4}; 23 is {6,8,9}; 24 is {7,8,9}.
• Four cells: 10 is {1,2,3,4}; 30 is {6,7,8,9}.

You do not need to memorize them all. Simply recognising that a small cage with a very high or very low total is tightly constrained will point you to where the puzzle opens up first.

Everything the classic game gives you

• Pencil notes for tracking candidates in tight cages.
• Hint, undo, redo, erase and a pause button with a running timer.
• Three difficulty levels, set by cage size and how much the sums give away, with a fresh unique board each game.
• Automatic saving, plus the site's light and dark theme.

Ready for it?

Killer Sudoku rewards patience more than speed, so take your time and let one deduction lead to the next. If you want to warm up first, the plain grid at Sudoku AZ and the graded Expert Sudoku are good preparation. For a change of texture rather than a change of difficulty, Color Sudoku and Flower Sudoku keep the logic while changing the look.