Arithmetic & Logic Variant
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Daily Killer Sudoku: Play Free Expert Sum Puzzles Online

Looking for a challenge beyond classic 9x9 grids? Killer Sudoku (also known as Sum Sudoku) combines pure placement logic with mental arithmetic. Using dotted cages with target sum totals, you must solve the entire board while obeying both classic Sudoku rules and cage math constraints.

The 3 Fundamental Rules of Killer Sudoku

Rule 1

Classic Sudoku Base

Every row, column, and 3x3 block must contain the numbers 1 to 9 with no repetitions.

Rule 2

Cage Sum Totals

The numbers inside each dotted cage line must add up precisely to the small number printed in its top-left corner.

Rule 3

No Cage Duplicates

No number may appear more than once inside the same cage, even if the cage crosses into another 3x3 box.

The Secret Weapon: The Rule of 45

The single most important mathematical strategy in Killer Sudoku is the Rule of 45. In every standard 9x9 Sudoku, the sum of digits 1 through 9 equals exactly 45:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

Because every row, column, and 3x3 block sums to 45, if a set of cages covers an entire 3x3 block except for one sticking-out cell, you can instantly calculate that cell's digit by subtracting the cage sums from 45! This technique (known as the "Innie/Outie" method) cracks open 90% of expert killer puzzles.

Killer Sudoku Unique Combinations Cheat Sheet

Always scan for cages that only have a single mathematical combination of digits:

Sum 3 (2 cells)[ 1, 2 ] strictly
Sum 4 (2 cells)[ 1, 3 ] strictly
Sum 16 (2 cells)[ 7, 9 ] strictly
Sum 17 (2 cells)[ 8, 9 ] strictly
Sum 6 (3 cells)[ 1, 2, 3 ] strictly
Sum 7 (3 cells)[ 1, 2, 4 ] strictly
Sum 23 (3 cells)[ 6, 8, 9 ] strictly
Sum 24 (3 cells)[ 7, 8, 9 ] strictly

Frequently Asked Questions (Killer Sudoku)

Is Killer Sudoku harder than regular Sudoku?

At first glance, yes—because opening boards usually have zero prefilled numbers! However, cage sums provide powerful mathematical clues. Once you memorize common combinations and apply the Rule of 45, Killer Sudoku is often more satisfying and intuitive than traditional puzzles.

Can a cage contain repeating numbers?

No. By official Killer Sudoku tournament rules, no digit may repeat inside the same dotted cage, even if the cage spans across multiple rows or 3x3 blocks.

What is the "Rule of 45" in Killer Sudoku?

Since every row, column, and 3×3 block must contain digits 1 through 9, the sum of any complete row, column, or nonet is always exactly 45. By comparing the sum of all cages fully inside a unit against 45, you can instantly determine the exact value of single cells protruding in ("innies") or out ("outies").