Killer sudoku keeps every rule of the classic 9×9 puzzle and adds one more layer: cages. A cage is a group of cells inside a dotted outline with a small number in its corner, and the digits inside it must add up to that number. Our killer puzzles start with no digits printed in the grid at all. Everything you place comes from the cage totals and the usual row, column and box rules.
That sounds harder than it is. The arithmetic is limited to small sums of different digits, and a handful of cages on every board can only be filled one way. This guide covers the rules, then the first moves in the order you will use them.
The rules
- Fill every cell of the 9×9 grid with a digit from 1 to 9.
- Each row, each column and each of the nine 3×3 boxes contains every digit from 1 to 9 exactly once.
- The digits in each cage add up to the number in its corner.
- A digit can't appear twice in the same cage, even when the cage crosses from one box into another.
How a grid with no digits can have one answer
Every cell belongs to exactly one cage, so the cage totals across the whole grid add up to 405, which is nine rows of 45. The cage outlines and totals carry the same information that given digits carry in a classic grid, just in coded form. Every puzzle on this site has been checked by a solver that proves there is exactly one way to fill it, and a second solver confirms it can be finished by logic without guessing.
Cages on our puzzles run from one cell to five. A one-cell cage is simply a given digit: a cage of 7 around a single cell means that cell is 7. Write those in first.
First move: find the cages that only work one way
Some totals can be made from just one set of digits. Two cells adding up to 3 must be 1 and 2, because 3 = 1+2 is the only option without repeating a digit. Two cells making 4 must be 1 and 3. At the top end, two cells making 17 are 8 and 9, and 16 is 7 and 9, since 8+8 would repeat.
Three-cell cages have their own short list. A total of 6 is 1+2+3, 7 is 1+2+4, 23 is 6+8+9 and 24 is 7+8+9. Pencil those digits into every cell of the cage. You don't yet know which cell gets which, but you now know what the cage holds, and that is often enough to place digits elsewhere.
Keep the killer sudoku cheat sheet open for the first few games. It lists every combination for every cage size, with these one-way totals highlighted.
Second move: let cages and houses work together
A cage that lies inside one row, column or box uses up its digits in that house. Say a two-cell cage of 3 sits in row 2. Its cells hold 1 and 2 between them, so no other cell in row 2 can be 1 or 2. If the cage also lies inside one box, the same goes for the rest of that box.
Placed digits shrink cages in the other direction. A two-cell 10 could be 1+9, 2+8, 3+7 or 4+6. If both of its cells sit in a box that already holds 1, 2 and 3, the first three pairs are gone and the cage is 4 and 6. When one cell of a cage is the only cell left in its row that can take 4, it is the 4, and the other cell is 6.
The last cell of a cage is a simple subtraction. If a three-cell 14 already has a 9 and a 1 in it, the third cell is 4.
Third move: the rule of 45
Every row, column and box adds up to 45. That gives you a sum for free whenever cages nearly line up with a house. Suppose four cages sit wholly inside a box and add up to 40, and the box's ninth cell belongs to a cage that pokes out into the next box. That single cell, called an innie, must be 5, because 45 minus 40 is 5.
It works from the outside too. If a set of cages covers a whole box plus one extra cell outside it and their totals add up to 52, the extra cell, an outie, is 7. Easy puzzles on our site use this single-cell version of the rule, so it is worth checking every box, row and column for it once the obvious cages are done.
Finishing off with singles
The rest of an easy killer is classic sudoku logic. A naked single is a cell with only one candidate left. A hidden single is a digit with only one possible cell left in a row, column or box. After every new digit, look at its row, column, box and cage again: in killers a placement often finishes a cage sum as well as removing a candidate.
Use pencil marks freely. Note the possible digits in small cages as soon as you work them out, and trim them as the grid fills. The Pencil button on the board does this, and Undo takes back a slip.
What changes at higher levels
Our grader solves every puzzle the way a person would, cheapest technique first, and the level is the hardest technique it needed. Easy puzzles need only cage combinations, singles and one-cell innies and outies. Medium adds pointing and claiming, naked pairs, cage/house interactions and the rule of 45 with two leftover cells. Hard brings the rule of 45 across several rows or boxes at once, plus hidden pairs and naked triples. Expert adds patterns such as the XY-wing, the swordfish and simple coloring.
Those later techniques are covered with worked examples in our killer sudoku strategy guide.
Where to start
Begin with the easy killer sudoku puzzles until finding the one-way cages becomes a habit, then try the daily killer sudoku, which changes every day. If you prefer paper, the printable killer sudoku packs come with the answers on the last pages.
A good routine for any killer: write in one-cell cages, pencil in every one-way cage, check each house for a 45-rule innie or outie, then work singles until the next cage gives way. Repeat that loop and most easy and medium grids come out cleanly.