Kakuro

How to Play Kakuro

Kakuro is a cross-sum number deduction puzzle. The grid contains two types of cells: white cells where you fill in digits, and black cells that carry clue numbers. Each black clue cell is divided diagonally — the number in the bottom-left triangle is the across clue for the white run to its right, and the number in the top-right triangle is the down clue for the white run below it.

Your goal is to fill every white cell with a digit from 1 to 9 so that two rules are satisfied simultaneously: every run's digits must sum to its clue, and no digit may be repeated within the same run. Because every white cell belongs to exactly one across run and one down run, placing a digit must satisfy both constraints at once. Every puzzle has a unique solution reachable by pure logic — no guessing required.

Strategy Tips

• Start with the most constrained runs. A run of 2 cells with clue 3 can only be {1,2}; a run of 2 with clue 17 can only be {8,9}. Short runs with extreme clues have just one possible combination — fill those first.
• Use the combination table. For every run length and clue value, there are only a handful of valid digit sets. Knowing that a 3-cell run summing to 7 must use {1,2,4} rules out five digits immediately.
• Cross-run elimination. Once you know a digit is in a run but not which cell, look at the perpendicular run through each candidate cell. If placing that digit would make the perpendicular run impossible, you've narrowed the position.
• Pencil marks are your friend. Press P (or tap the Pencil button) to enter candidate digits in small type. Fill in candidates for every cell first, then prune them as you apply constraints — confirmed digits will emerge.
• Scan for forced digits. If all but one candidate has been eliminated from a cell by its two runs, that cell is forced. Work outward from forced cells since they eliminate candidates in connected runs.

What Makes Kakuro Unique

Unlike Sudoku — which constrains rows, columns, and boxes by position — Kakuro constrains variable-length runs by arithmetic. Every run is a mini-puzzle in itself, and the interlocking structure means a deduction in one corner can propagate to the opposite side of the board. The paper-warm aesthetic here — newsprint cream background, red clue numbers, pencil-grey player digits — echoes the Japanese newspaper origins of the puzzle, first popularised by Nikoli in 1983 under the name カックロ (kakkuro).