Kakurasu

Kakurasu is a binary grid puzzle where the player must decide which cells in each row and column to shade. Each row and column has a target sum, and the value of a shaded cell is determined by its position: the first cell in a row or column is worth 1, the second is worth 2, and so on. The shaded cells in each row and column must add up to the given target. It combines the satisfaction of Kakuro's arithmetic with a simpler yes/no decision per cell.

Rules

1. The grid is NxN (commonly 5x5 to 9x9).
2. Each row and column has a target number displayed at the edge.
3. Decide which cells to shade (fill) and which to leave empty.
4. A shaded cell's value equals its position number in that direction: column 1 = value 1, column 2 = value 2, etc. for row clues; row 1 = value 1, row 2 = value 2, etc. for column clues.
5. The values of all shaded cells in a row must sum to that row's target.
6. The values of all shaded cells in a column must sum to that column's target.

Strategies

• Zero Target: If a row or column has a target of 0, no cells in that line are shaded.
• Maximum Sum: If the target equals the sum of all positions (1+2+...+N), all cells in that line must be shaded.
• Unique Decomposition: Some targets can only be achieved by one combination of positions. For example, in a 5-column row, a target of 1 can only be achieved by shading column 1.
• Cross-referencing: A cell belongs to both a row and a column. If shading it would make either sum impossible, it must remain empty.
• Elimination: Try removing positions that would overshoot the target and see which combinations remain valid for both row and column constraints.

Kakurasu originated in Japan and was popularized by puzzle magazines in the 2000s. The name is a Japanese portmanteau combining "kasan" (addition) and "kurasu" (a phonetic adaptation suggesting "cross" or grid-based puzzles).

The puzzle emerged as part of the wave of Japanese logic puzzles that followed the international Sudoku boom. Publishers like Nikoli and Puzzler were actively developing new puzzle formats to satisfy the growing appetite for logic challenges.

Kakurasu is less well-known than its cousins Sudoku and Kakuro, but it has a dedicated following among puzzle enthusiasts who appreciate its unique combination of binary decisions (shade or don't shade) with positional arithmetic. The puzzle appears regularly in online puzzle communities and puzzle competition warm-up rounds.

Its relatively simple rules and visual clarity make it particularly well-suited to digital formats, where the immediate feedback of highlighting row/column sums helps players learn the logic quickly.