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中文Kropki has exactly three signals. A white dot between two cells means they differ by exactly 1 (like 3·4). A black dot means one is double the other (like 2·4). And no dot means neither relation holds — the missing dot is a real constraint, not an absence of information. A 1-2 pair satisfies both relations; by convention it is marked with a black dot. Rows and columns still contain each number once, like any Latin square.
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| Rule | What it means |
|---|---|
| Latin square | Every row and every column contains each number exactly once. |
| White dot | The two cells differ by exactly 1 — consecutive numbers in either order. |
| Black dot | One cell is exactly double the other (1·2, 2·4 on a 5×5). |
| No dot | Neither relation holds — this negative constraint eliminates as many candidates as the dots do. |
| 1-2 convention | 1 and 2 both differ by one and double — the pair is marked black by convention. |
On a 5×5 only 1·2 and 2·4 can sit under a black dot, so every black dot forces a 2 into one of its two cells. A chain of two black dots is even stronger: it must be 1-2-4.
A cell next to a 3 with no dot between them cannot be 2, 4, or 6. On boards with few or zero givens — most dailies here start empty — the dotless edges do most of the work.
White-dot chains alternate odd/even. Trace a chain from any placed number and half the candidates disappear along the whole chain.
Most daily kropki boards here start with zero given digits — the dot pattern alone determines a unique solution, and the client enforces the negative constraint too (many sites don't). 450 daily 5×5 boards plus 320 free-play boards, each machine-verified for a unique deduction-reachable solution before publication.
A white dot between two cells means the numbers differ by exactly 1. A black dot means one number is exactly double the other. If there is no dot, neither relation holds — that negative constraint is a full part of the rules.
1 and 2 satisfy both relations (they differ by 1, and 2 is double 1). The standard convention, used here, is to mark a 1-2 pair with a black dot.
Yes. The dot and no-dot pattern can force a unique solution on its own — most daily boards on this site start completely empty and are machine-verified to be solvable by pure deduction.
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