Kropki Sudoku
A popular Sudoku variation where white and black dots mark consecutive and half-digit relationships
Kropki Sudoku (meaning "Dots" in Polish) is one of the most popular Sudoku variations. There are very few Sudoku types and number puzzle types in which no given hint is required to solve the puzzle. Kropki is one of such puzzle types, wherein most puzzles have no numbers given as hints. In Kropki puzzles, white dots mark consecutive digits, and black dots mark digits where one is half of the other. The dot between 1 and 2 can be either white or black. This collection includes Kropki Sudoku puzzles of various sizes (9x9, 6x6, 7x7, 5x5, and 4x4), along with Double Kropki Sudoku, Reverse Kropki Sudoku, and Dots Sudoku variations. This page contains links to all Kropki Sudoku puzzles and their variations published on this website.
Rules of Kropki Puzzle
Fill in the grid with digits 1 – N, where N is the size of the grid, so that each row and column contains each digit exactly once. If two consecutive digits appear in two neighbouring cells, they are separated by a white dot. If the digit in a cell is half of the digit in the neighbouring cell, then they are marked by a black dot. The dot between 1 and 2 can either be white or black.
Rules of 9x9 Kropki Sudoku
Classic Sudoku Rules apply. Additionally, if the absolute difference between two digits in neighbouring cells equals 1, then they are separated by a white dot. If the digit is half of the digit in the neighbouring cell, then they are separated by a black dot. The dot between 1 and 2 can be either white or black.
Rules of 6x6 Kropki Sudoku
Mini Classic Sudoku Rules apply. Additionally, if the absolute difference between two digits in neighbouring cells equals 1, then they are separated by a white dot. If the digit is half of the digit in the neighbouring cell, then they are separated by a black dot. The dot between 1 and 2 can be either black or white.
Why Solve Kropki Sudoku?
- Features a unique dot-based logic that makes it visually distinctive and fun.
- One of the few puzzle types where no given hints are required to solve.
- Available in multiple grid sizes from 4x4 to 9x9.
- Includes exciting variations: Double Kropki, Reverse Kropki, and Dots Sudoku.
- Great for all skill levels, from beginners to advanced solvers.
- Builds logical deduction and arithmetic skills through dot relationships.
Key Techniques for Solving Kropki Sudoku
- Understand the dots: white dot = consecutive digits (difference of 1), black dot = one digit is half of the other.
- Identify dot pairs white dot pairs: (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9). Black dot pairs: (1,2), (2,4), (3,6), (4,8).
- Note the 1-2 ambiguity; the dot between 1 and 2 can be either white or black.
- Apply converse logic if no dot is present, adjacent cells cannot be consecutive or have a half-digit relationship.
- Apply standard Sudoku logic; always apply row, column, and box eliminations.
- Check your work, verify that all white dots connect consecutive digits and all black dots connect half-digit relationships.
⚪ 9x9 Kropki Sudoku Puzzles
⚪ 6x6 Kropki Sudoku Puzzles
⚪ Kropki Variations
⚪ Kropki Puzzles (Non-Sudoku)
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Frequently Asked Questions
What is Kropki Sudoku?
Kropki Sudoku (meaning "Dots" in Polish) is a Sudoku variation where white and black dots are placed between adjacent cells. A white dot means the two digits are consecutive (differ by 1). A black dot means one digit is half of the other. If no dot is present, neither relationship applies.
What do white and black dots mean in Kropki Sudoku?
A white dot indicates that the two adjacent digits are consecutive (e.g., 3 and 4, 7 and 8). A black dot indicates that one digit is exactly half of the other (e.g., 2 and 4, 3 and 6, 4 and 8). The dot between 1 and 2 can be either white or black.
What is the difference between Kropki Puzzle and Kropki Sudoku?
Kropki Puzzle is a Latin square puzzle where each row and column contains each digit exactly once, without the 3x3 box constraint. Kropki Sudoku adds the Classic Sudoku 3x3 box constraint to the Kropki dot rules. This collection includes both types.
What are the variations of Kropki Sudoku?
This collection includes several variations: Double Kropki Sudoku (uses two sets of dots), Reverse Kropki Sudoku (the converse rule applies), and Dots Sudoku (a variation with different dot meanings). Each variation adds unique twists to the standard Kropki Sudoku rules.
Where can I find more Sudoku variations?
The Sudoku Variations Main Page is the central index for all Sudoku variant types available on Fun With Puzzles. It covers a wide range of constraint-based variants and is the best place to discover new Sudoku challenges.
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