Kropki

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Complete the Latin grid using white and black dots that relate neighbouring values.

1. Fill each row and column with the numbers from 1 to the board size without repetition.
2. A white dot means the neighbouring values are consecutive; a black dot means one is exactly double the other. In Blupoli, a pair that satisfies both relations is shown with a black dot.
3. If two adjacent cells have no dot between them, their values are neither consecutive nor in a 1:2 ratio.

• Black dots require a 1:2 relationship and white dots consecutive values; no dot rules out both relationships.
• Start with black dots because the 1:2 relation sharply limits the candidates.
• Combine each dot with row and column uniqueness before committing to a value.
• A missing dot is also information: it rules out both consecutive and double pairs.

We do not yet have a sufficiently verified account of this game’s origins. Rather than guess, we avoid attributing a date or creator without reliable evidence.

• Start with black dots because the 1:2 relation sharply limits the candidates.
• Combine each dot with row and column uniqueness before committing to a value.
• A missing dot is also information: it rules out both consecutive and double pairs.

• Where should I begin? Black dots require a 1:2 relationship and white dots consecutive values; no dot rules out both relationships.
• What makes this game different? If two adjacent cells have no dot between them, their values are neither consecutive nor in a 1:2 ratio.