Medium Kropki Sudoku
5
2
4
7
8
6
5
4
1
6
1
5
8
9
1
2
4
8
1
3
4
6
3
5
8
9
2
8
2
4
3
6
How to play Kropki Sudoku
Standard Sudoku rules apply. Black dot between two adjacent cells: one digit is exactly double the other. White dot: the two digits are consecutive (differ by 1). No dot: neither condition applies.
About Kropki Sudoku
Difficulty
★★★☆☆
3/5
Constraint Type
Cell Relationships
Typical Givens
18–24
Avg. Solve (Medium)
18 min
Kropki Sudoku places dots between pairs of adjacent cells. A white dot means the two digits differ by exactly 1 (consecutive). A black dot means one digit is exactly double the other (e.g., 2 and 4, or 3 and 6). Where no dot appears, neither condition applies. Some Kropki puzzles use the 'negative constraint' where the absence of a dot guarantees neither condition holds, giving even more information.
Solving Techniques
| Technique | Description | Level |
|---|---|---|
| White Dot Pairs | White dots mark consecutive digit pairs: (1,2), (2,3), …, (8,9). Cross-reference with row and column constraints. | Beginner |
| Black Dot Pairs | Black dots mark double-relationship pairs: (1,2), (2,4), (3,6), (4,8). Only these four combinations are valid. | Beginner |
| Negative Constraint | No dot between two cells means they are neither consecutive nor in a 1:2 ratio — a powerful elimination on every unmarked adjacent pair. | Intermediate |
| Dot Chain Analysis | A sequence of connected dots forms a digit-value chain. Enumerate valid digit sequences for the entire chain simultaneously. | Advanced |
| 1-2-4 and 2-4-8 Chains | A black dot adjacent to a white dot often forces the common 1→2→4 or 2→4→8 chain. | Intermediate |
Average Solve Time by Difficulty
Easy
8 min
Medium
18 min
Hard
35 min
Expert
62 min