How to Solve Killer Sudoku Puzzles

The rules in one minute

Now and then a cage has a single square. Its sum is its digit, so the page fills it in for you, and it works like a given digit in an ordinary sudoku.

Sizes and difficulty

Every daily grid has exactly one solution, and it is checked when it is made: the rules described here, applied without any guessing, fill in every square.

Cage combinations

A cage of a given size and sum can only hold certain sets of digits. Two squares adding up to 10 can be 1 and 9, 2 and 8, 3 and 7 or 4 and 6, but never 5 and 5, because a cage never repeats a digit. The smallest and largest sums are the most useful, because they leave only one set:

The pattern is easy to remember: the lowest two sums and the highest two sums of any size have one answer each. For the sums in between, count the sets. A three-square 9 has three: 1 2 6, 1 3 5 and 2 3 4. If the row already has a 1, only 2 3 4 is left.

Show cage combinations, in the options, lists the sets the selected cage can still hold, given the digits already placed in it. It is a good way to learn the sums.

The rule of 45

Every row, column and box adds up to 1 + 2 + … + 9 = 45. That one fact gives Killer Sudoku its signature move. Pick a box and add up the cages lying wholly inside it. If they cover all but one square, that square is 45 minus their total. A square found this way is called an innie.

The same works in reverse. If the cages touching a row add up to more than 45, the extra belongs to the squares of those cages that stick out of the row. A single square sticking out, an outie, is the difference: cages touching row 1 adding up to 51, with one square hanging down into row 2, put a 6 in that square. The rule also stretches to several units: two rows add up to 90, three rows (a band of three boxes) to 135, and the same for columns. When two squares are left over, their sum is known, which is often enough to narrow both.

Cages and units together

Cage combinations become stronger when a cage sits inside one row, column or box. A three-square 7 lying along a row takes 1, 2 and 4, so no other square of that row can hold them, exactly like a naked triple in sudoku. A digit that a cage must contain, and that can only go in the part of the cage inside one box, is removed from the rest of that box.

Cages also work together. If a box holds a two-square 3 and a two-square 17, its 1, 2, 8 and 9 are all spoken for, so the other five squares of the box can only hold 3 to 7. Notes help here: write the possible digits in each square of a cage, and let the row, column and box clear them.

A solving routine

1. Fill the obvious cages. Single squares, then cages with one possible set, then the 45 innies and outies of each box.
2. Write notes. For each cage, note the digits its sets allow. Leave Notes clear themselves switched on so that every digit you place clears itself from its row, column, box and cage.
3. Scan like a sudoku. A digit with one place left in a row, column or box goes there, and a square with one note left is solved.
4. Return to the sums. Every placed digit lowers what a cage still needs: a three-square 15 with a 9 already in it needs two digits making 6, which is 1 and 5 or 2 and 4.

Repeat until the grid fills. When nothing moves, look for a unit the cages almost cover: the rule of 45 is rarely far away.

Common mistakes

• Repeating a digit in a cage. The digits of a cage are always different, even when the cage crosses from one box into another. Show mistakes marks a repeat at once.
• Adding the 45 rule to the wrong cages. Only cages lying wholly inside the unit count towards the innie. A cage that pokes out belongs to the outie side.
• Losing track of a part-filled cage. The line above the grid shows the digits placed in the selected cage so far, and a cage already at or past its sum before it is full is flagged.

Speed habits

• Start at the extremes. Small sums in small cages and big sums in small cages settle first.
• Use the keyboard on a computer. Arrow keys move, digits fill, N switches notes, Backspace erases and Ctrl+Z undoes.

Scoring and the leaderboard

Killer Sudoku is ranked by time, fastest first; fewer entries break ties. The clock starts with your first move, the grid is checked the moment the last square is filled correctly, and only a member's first solve of the day counts for the leaderboard. Practice puzzles from Play more are never ranked. If you like the sums, Kakuro is built on the same digit sets, and Calcudoku adds the other three operations.