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A 6×6 number puzzle told entirely in dots. Fill every row and column with 1 to 6: a white dot joins two consecutive numbers, a black dot joins a number and its double, and where there is no dot the pair is neither. Every board has one solution you can reach by logic alone — how fast can you find it?
The board is a 6×6 grid. Fill it so that every row and every column contains each number from 1 to 6 exactly once, as in Sudoku but without boxes. A few squares may start with a number already in gold; those cannot be changed.
The dots between neighbouring squares are the clues. A white dot means the two numbers differ by exactly one, like 3 and 4 or 6 and 5. A black dot means one number is exactly twice the other, like 3 and 6 or 2 and 4. The pair 1 and 2 is both consecutive and a double, so it can sit under either colour. Every dot is shown, so a missing dot is a clue too: two neighbours with no dot between them are neither consecutive nor a double.
Press Start and the clock begins. Tap a square to select it, then tap a number on the pad below the board. Tapping the same number again clears it, and ⌫ erases the square. Turn on Notes to jot small pencil marks instead: in notes mode each number you tap is added to or removed from the selected square's marks. When you place a real number, that number is removed automatically from the notes in the same row and column. Squares holding the same number as the one you selected are tinted so you can spot them quickly.
Mistakes are shown as soon as they appear: a repeated number in a row or column, or two filled neighbours that break their dot, turn red, and a broken dot gets a red ring. The puzzle is complete the moment every square is filled without a single conflict.
Your score is the time you took, and lower is better. The clock is real time, so it keeps running if you switch apps. Your best time is kept on this device, and you can save any finished time to the Hall of Fame. On a keyboard you can also type 1–6, use the arrow keys to move, Backspace to erase and N to toggle notes.
Start with the black dots, because so few pairs can sit under them. A black dot always holds 1 and 2, 2 and 4, or 3 and 6 — nothing else. That means 5 can never touch a black dot, and a black dot that already has a 4 or a 6 on one side tells you its partner at once (2 or 3). When three squares in a straight line are joined by two black dots, the middle one must be 2, with 1 and 4 at the ends, because 2 is the only number with two different partners.
The empty spaces between squares are just as useful. With no dot, a pair can be neither consecutive nor a double. Work out what that forbids: next to a 3 without a dot you cannot have 2, 4 or 6, so the neighbour must be 1 or 5. Next to a 2 without a dot you cannot have 1, 3 or 4. The middle numbers 2, 3 and 4 are the most restricted, so look for squares surrounded by plain edges — they are often the quickest to pin down.
White dots form chains of consecutive numbers. A row of three squares joined by two white dots holds three numbers in a run, such as 2-3-4 or 5-4-3, so the ends of a long white chain can only be certain values. Combine that with the row and column rule: if a row already has its 1 and 6 placed elsewhere, a four-square white chain in it must be 2-3-4-5 in one direction or the other.
Use notes when two or three options remain, and let the automatic clean-up do the bookkeeping: every number you place removes itself from the notes in its row and column. Kropki — Polish for "dots" — is usually printed on a 9×9 grid in puzzle-championship and Sudoku-variant collections; this 6×6 version keeps exactly the same logic at a size you can solve in a few minutes on a phone. Every board here is checked to have a single solution that can be found by reasoning alone, without guessing.