Medium Kropki Sudoku

Black dots signal a doubling relationship; white dots mean consecutive digits. Unmarked pairs carry equally powerful information. Free online.

Easy Medium Hard Expert

Kropki Sudoku at medium difficulty. Dot-pair enumeration combines with standard techniques — the absence of dots is as informative as the dots themselves.

3
4
9
7
8
6
1
5
3
8
9
1
9
1
8
7
3
8
2
9
5
7
4
1
4
9
6
3
5
9
7
2
Mistakes
0/3
Score
-
Time
00:00
Try Hard Kropki Sudoku →
Progress0%

What is Kropki Sudoku?

Difficulty
★★★☆☆
3/5
Constraint Type
Cell Relationships
Typical Givens
18–24
Avg. Solve (Medium)
18 min

Solving Techniques for Medium Level

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
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

Master these, then take on Hard Kropki Sudoku to learn Advanced techniques.

Techniques to Master at Medium

  • Hidden Singles technique — The no-dot rule strips consecutive and double partners from every unmarked edge — after applying it across a unit, the surviving digit positions are frequently singles.
  • Obvious Pairs technique — A white-dot pair narrowed to {2,3} acts as an obvious pair for its unit while the dot itself remembers the order constraint — two techniques in one marking.

Average Solve Time by Difficulty

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

Related Variants

XV Sudoku

Both mark adjacent-cell relationships with a powerful negative rule — XV's sum markers play exactly like kropki's dots.

Consecutive Sudoku

Isolates the white-dot half of kropki: bars mark consecutive neighbours and silence means never consecutive.

Greater Than Sudoku

Adjacent-cell relationships again, but as inequalities — order information instead of difference and ratio.

Frequently Asked Questions — Medium Kropki Sudoku

What techniques are most useful for medium Kropki Sudoku?
Medium puzzles require systematic dot-pair enumeration. For each dot, list all digit pairs that satisfy the constraint given what is already known in that row, column, and box. Then eliminate pairs that conflict with other dots nearby. Naked pairs within a row or box — combined with dot constraints — give the strongest breakthroughs.
How do I use the absence of dots at medium difficulty?
At medium difficulty, no-dot constraints become crucial. If two cells separated by no dot both have candidates from a restricted set, you can eliminate any pairs that would be consecutive or in a 1:2 ratio. This is especially powerful when combined with box logic to whittle down candidates to a single option.
Can the same digit appear on both sides of a dot?
No. Standard Sudoku rules still apply — every row, column, and 3×3 box must contain each digit 1–9 exactly once. So both cells of a dot-pair must hold different digits. A black dot can never have the same digit on each side, nor can a white dot.
How do dot constraints interact with naked pairs?
If two cells in a box are linked by a white dot and their candidates are restricted to {3, 4}, those two cells form a naked pair for the box. All other cells in that box can have 3 and 4 removed from their candidates. Kropki's dot constraints often force naked pairs that would not appear in standard Sudoku.
How long does a medium Kropki Sudoku take?
Most players finish medium Kropki Sudoku in 20–30 minutes. The puzzle is designed so that systematic dot-pair enumeration combined with standard techniques is enough — no trial and error needed. If you're stuck, go back to any dot you haven't fully enumerated.

More questions? See the full Kropki Sudoku guide.