Logic Masters Deutschland e.V.

Kropki Squares

• Normal sudoku rules apply.
• Killer Cages: Digits in cages cannot repeat.
• Unique Cells: Digits in the shaded cells must all be different.
• Kropkis: Grey dots on a corner indicate that in the 2x2 of surrounding cells, there must be two cells whose digits form a 1:2 ratio with each other and the other two cells must contain consecutive digits. See examples below.

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Examples:

• All four digits must be used in a 2x2 to satisfy a grey kropki. In the example below on the left, even though 43 is consecutive, 26 is not in a 2:1 ratio. Additionally, even though 36 is in a 2:1 ratio, 42 is not consecutive. On the other side, 23 is consecutive and 48 are in 2:1 ratio, therefore that kropki square is valid.

• 1 and 2 can be used as either the consecutive constraint or the 2:1 constraint in a kropki square. In the example below, on the left 36 are 2:1 and 12 are consecutive so the kropki square is valid. On the right, 12 are 2:1 and 34 are consecutive so the kropki square is valid. In the puzzle, it is up to the solver to determine which role 12 needs to fill.