Cages: Killer Sudoku Explained (and How to Open One) 🔢

The rules

All the normal Sudoku rules apply: 1–9 once per row, column and 3×3 box. On top of that, the grid is divided into dotted cages. The digits in a cage must add up to the small number printed in its corner, and no digit repeats inside a cage.

The rule of 45

This is the technique that makes Killer Sudoku click, and it's almost too simple.

Every row, column and box contains 1 through 9 exactly once. So every row, column and box sums to 45.

Now look at a box where three cages sit entirely inside it and a fourth cage pokes out by one cell. Add the three inside cages, add the poking cage, subtract 45, and you have the value of the cell sticking out. One arithmetic step, one placed digit, no candidate analysis at all.

The same works across two or three boxes (sum 90 or 135), which is how you crack the hard boards.

Cage combinations

Same idea as Kakuro: some cages have only one possible digit set.

• 3 in 2 cells → 1+2. 4 in 2 → 1+3. 16 in 2 → 7+9. 17 in 2 → 8+9.
• 6 in 3 → 1+2+3. 7 in 3 → 1+2+4. 23 in 3 → 6+8+9. 24 in 3 → 7+8+9.

A 17-in-2 cage sitting in a box immediately removes 8 and 9 from every other cell in that box, which is usually worth more than a placed digit.

One more that catches people out: a cage that lies entirely within one row and one box can't repeat digits — but a cage that spans two boxes still can't repeat either, because the no-repeat rule is a property of the cage, not of the region it sits in.

About our version

99 levels with a difficulty curve that grows the number of cages and shrinks the given digits. Notes, unlimited undo, hints, and cage sums that stay readable on a phone. Every board is verified to have exactly one solution.

It runs in your browser, works offline once loaded, needs no account, and costs nothing.

Questions people actually ask

What's the difference between Killer Sudoku and normal Sudoku?
Killer Sudoku starts with almost no given digits. Instead it has dotted cages with target sums, and no digit may repeat inside a cage. All the usual row, column and box rules still apply.

Can a digit repeat inside a cage?
No, never — even if the cage spans two boxes.

Where do I start on a Killer Sudoku?
Look for two-cell cages with extreme sums (3, 4, 16, 17) and for boxes where the cages almost tile the box, so the rule of 45 gives you a cell outright.

Keep reading

• Sudoku Online: How to Play and How to Get Faster 🔢 — Four difficulties, pencil marks, and a hint that teaches instead of just filling a square. Plus the three techniques that get you past Easy.
• Kakuro: The Cross-Sum Puzzle Worth Learning 🔢 — A crossword made of sums. Steeper than Sudoku, more satisfying, and the entire game opens up once you memorise about six number combinations.
• Logic Puzzle Games: A Guide to the 12 in Go Brain 🧠 — Sudoku, Kakuro, Nonogram, Crowns and eight more. What separates a real deduction puzzle from a guessing game, and which to start with.