Hard Killer Sudoku

Cage sums meet classic Sudoku logic. Digits in each cage must total the clue — no repeats allowed. Free, no login required.

Easy Medium Hard Expert
Mistakes
0/3
Score
-
Time
00:00
18
6
22
12
8
25
19
7
7
19
17
13
10
14
9
7
3
13
5
4
8
16
18
7
13
14
4
27
7
9
10
20
4
10
Try Expert →
Progress0%
34 cages All Killer →
How to play Killer Sudoku
The board starts with pre-filled digits as clues. Your clues are the cage sums (small numbers in cell corners). Fill each cage so the digits sum to that total, with no repeats within any cage. All standard Sudoku rules still apply (1–9 in every row, column and 3×3 box).
How to Play Killer Sudoku →

Killer Sudoku - Complete Guide

Difficulty Overview
Level Given digits Cages Avg. solve time
Easy ~26 ~28-32 5-10 min
Medium ~18 ~30-36 10-20 min
Hard ~8 ~34-40 20-40 min
Expert 0 ~36-45 40-90 min
Cage Sum Limits
Cage size Min sum Max sum Forced?
1 cell 1 9 Yes (unique)
2 cells 3 17 At extremes
3 cells 6 24 At extremes
4 cells 10 30 At extremes
5 cells 15 35 At extremes
9 cells Always 45 Yes

Forced cage combinations you must memorise

2-Cell cages - Forced sets
Sum Only possible set
3 {1, 2}
4 {1, 3}
16 {7, 9}
17 {8, 9}
3-Cell cages - Forced sets
Sum Only possible set
6 {1, 2, 3}
7 {1, 2, 4}
23 {6, 8, 9}
24 {7, 8, 9}
4-Cell cages - Forced sets
Sum Only possible set
10 {1, 2, 3, 4}
11 {1, 2, 3, 5}
29 {5, 7, 8, 9}
30 {6, 7, 8, 9}
5-Cell cages - Forced sets
Sum Only possible set
15 {1, 2, 3, 4, 5}
16 {1, 2, 3, 4, 6}
34 {4, 6, 7, 8, 9}
35 {5, 6, 7, 8, 9}

Key solving techniques

45 Rule

Every row, column, and 3x3 box sums to 45. If all cages in a row are known except one cell, the missing value = 45 - (sum of all other cage totals in that row). This is the single most powerful Killer technique.

Innies and Outies

When a cage partially straddles a row/column/box boundary, the cells inside the boundary are "innies" and those outside are "outies." Their sum difference reveals exact values using the 45 rule, often resolving cells without any candidates.

Cage Overlap Counting

When a cage spans two boxes or rows, use subset counting to pin down which digits appear in the overlap region. Subtract partial cage sums to isolate individual cell values - Especially useful when the 45 rule leaves two unknowns.

Hard tip - Build a sum map before writing any candidates. Use the 45 rule on all rows, columns, and boxes simultaneously to generate innie/outie equations. Resolve overlapping cage regions before switching to candidate-based logic.

Frequently Asked Questions

Can digits repeat in a cage?
No - Every cage follows the no-repeat rule. Each digit appears at most once within any single cage.
What is the 45 rule?
Every row, column, and 3x3 box contains digits 1-9, summing to 45. Subtracting known cage sums within any unit reveals leftover cell values.
Is Killer Sudoku harder than Classic?
Generally yes - There are no given digits, so you rely entirely on cage arithmetic and elimination. Easy Killer is roughly equivalent to Medium Classic.
What are innies and outies?
When a cage crosses a unit boundary (row, column, or box), the cells inside that unit are called innies and those outside are outies. The sum difference between them and 45 reveals exact cell values.

What is Killer Sudoku?

Difficulty
★★★☆☆
3/5
Constraint Type
Cage Sums
Typical Givens
0 (all cages)
Avg. Solve (Hard)
38 min

Solving Techniques for Hard Level

Technique Description Level
Cage Sum Elimination Each cage has a fixed sum. Use the sum and the number of cells to calculate which digits are possible — e.g. a 2-cell cage summing to 3 can only be {1,2}. Beginner
No-Repeat Rule Digits cannot repeat within a cage. Combined with sum constraints, this eliminates many candidates immediately. Beginner
45 Rule Each row, column, and box sums to 45. Subtract known cage totals within a unit to find leftover cell sums — often isolating a single value. Intermediate
Innies and Outies An innie is a cage cell inside a unit whose sum reveals a digit; an outie is outside. These provide single-cell deductions without full candidate tracking. Intermediate
Cage Overlap Counting When a cage spans two boxes or rows, use subset counting to pin down which digits appear in the overlap cells. Advanced
Naked Subset in Cages If a group of cages within a unit accounts for exactly n cells using n digits, those digits are locked to those cells and removed from all other unit cells. Advanced

Ready for the ultimate test? Try Expert Killer Sudoku — the hardest puzzles on Sudoku.by.

Average Solve Time by Difficulty

Easy
8 min
Medium
18 min
Hard
38 min
Expert
70 min
Want a full walkthrough of rules, strategies, and solving steps? How to Play Killer Sudoku →

Frequently Asked Questions — Hard Killer Sudoku

What makes hard Killer Sudoku difficult?
Hard puzzles have longer cages with many possible digit combinations, fewer straightforward 45 Rule deductions, and require chaining multiple techniques together. Multi-cell innies and outies appear frequently, and you'll need advanced Sudoku techniques (hidden pairs, pointing pairs, naked triples) alongside cage arithmetic.
Should I use pencil marks for hard Killer Sudoku?
Absolutely. Hard puzzles cannot be solved reliably without pencil marks. Record all possible cage combinations for every cell and update them after each placement. Without notes, you'll lose track of which combinations have been eliminated and which remain valid.
What is a multi-cell innie/outie?
When a cage straddles a unit boundary with multiple cells on each side, you can still calculate the sum of the cells on one side using the 45 Rule extended to the other side. The result constrains a group of cells rather than a single one. Narrowing possible combinations for that group is the core hard-level technique.
How do cage overlaps help at hard difficulty?
When cages share a boundary with a box or overlap across two rows, the digit sets in each side are constrained by both the cage sum and unit totals. Cells that appear in two overlapping cages carry double constraints and are the best candidates for early hard-level deductions.
How long does a hard Killer Sudoku take?
Expect 40–75 minutes for hard puzzles. Experienced solvers who can apply the 45 Rule and multi-cell innie/outie analysis fluently can finish in 30–50 minutes. The key bottleneck is usually recognising which unit combination to apply the 45 Rule to next.

More questions? See the full Killer Sudoku FAQ.