kropki

Kropki, from the Polish word for dot, is a family of logic puzzles based on Latin-square style grids and dot clues. The puzzle appears in various sizes, most commonly as a 5x5, 7x7, or 9x9 grid, including Sudoku variants that use standard 3x3 subgrids.

In a typical kropki puzzle, each cell must be filled with numbers from 1 to n, where n equals the grid size. The objective is to ensure that every row and every column contains each number exactly once (and, in Sudoku variants, each 3x3 subgrid does as well). Dots are placed between orthogonally adjacent cells to indicate a relationship between the two numbers. A white dot means the two numbers are consecutive (they differ by 1). A black dot means one number is twice the other. If there is no dot between two adjacent cells, no specific relation is prescribed.

Solving a kropki puzzle combines Latin-square logic with the dot constraints. Solvers use digit placement elimination, row/column/box constraints, and the dot clues to deduce which values are possible in each cell. The presence of white or black dots can propagate through the grid, restricting options and guiding the placement of numbers. Pre-filled digits or strategically placed dots often shape the difficulty and solvability of a puzzle.

Kropki puzzles are part of the broader category of puzzle types that blend arithmetic relations with grid-based placement. The term reflects the central signaling element—the dots—that encode simple numeric relationships used to derive a unique solution.