Killer Sudoku

How to Solve Killer Sudoku — Beginner to Advanced Guide

5 min read  ·  Burmly

Killer Sudoku looks intimidating — a Sudoku grid covered in colored cages with small numbers in the corners. But once you understand how the cages work, the puzzle opens up in ways regular Sudoku cannot.

The rules

Killer Sudoku has all the standard Sudoku rules: digits 1–9 appear exactly once in each row, column, and 3×3 box. But there are also cages — groups of 2 to 5 connected cells, outlined in color. The number in the corner of each cage is the sum of all digits in that cage. No digit may repeat within a cage.

Key difference from regular Sudoku: there are no given digits. The cages are your only starting information. All 81 cells begin empty.

Starting with small cages

The most powerful starting point is a 2-cell cage with a small sum. A cage summing to 3 must contain 1 and 2 — there is no other way. A cage summing to 4 must contain 1 and 3. These "forced pair" cages immediately give you two digits in specific cells.

2-cell cage sum = 3 → must be {1,2} 2-cell cage sum = 4 → must be {1,3} 2-cell cage sum = 17 → must be {8,9} 2-cell cage sum = 16 → must be {7,9} 3-cell cage sum = 6 → must be {1,2,3}

Using the "45 rule"

Every row, column, and 3×3 box contains the digits 1 through 9, which sum to exactly 45. This is a powerful constraint. If all but one cage in a row is complete, the remaining cage's sum within that row is 45 minus the total of the other cages.

Eliminating possibilities with cage constraints

Even when you cannot determine exact values, cages eliminate candidates. If a cage in a column contains cells in only one row within a 3×3 box, then the remaining cells in that row within the box cannot contain any digits already placed in the cage.

The no-repeat rule within cages

This is often forgotten by beginners. A cage summing to 10 with 3 cells could be {1,2,7}, {1,3,6}, {1,4,5}, or {2,3,5} — but never {1,4,5} and {2,3,5} simultaneously. Once you eliminate some combinations via row/column constraints, the remaining options narrow quickly.

Keep reading
→ Killer Sudoku vs Regular Sudoku → Killer Sudoku Cage Combinations
Play Killer Sudoku →

Ready to put this into practice?

Play Killer Sudoku on Burmly — free, no ads, global leaderboard.

Play Killer Sudoku →