Kakuro
The mathematical cousin of the crossword, filling connected runs with unique digits 1–9 that sum up to clue numbers indicated in diagonal slashes.
HISTORICAL ORIGIN LORE
The Lineage of Kakuro
Published under the title Cross Sums in American puzzle magazines by Dell Publishing during the 1950s, the puzzle was imported to Japan by Nikoli in 1986 and named Kasan Kurosu (Addition Cross), which was abbreviated to Kakuro. In Japan, it remains the second most celebrated pencil puzzle after Sudoku.
SYSTEM MECHANICS & RULES
Rules & Cognitive Architecture
The board resembles a crossword grid with white playable cells and black clue cells divided diagonally.
The top-right number in a clue cell is the target sum for the horizontal run of white cells to its right.
The bottom-left number is the target sum for the vertical run of white cells below it.
Enter digits 1 through 9 into each white cell.
No digit may be repeated within any contiguous sum run.
Trained Mental Models
- ▸Integer partition memorization and prime sum combination recall
- ▸Intersecting set cross-referencing and parity balancing
- ▸Simultaneous multi-variable algebraic constraint satisfaction
INCLUDED FREE FOREVER
The Three Base Tiers
Gentle
5×5 and 6×6 grids featuring high-certainty sum pairs (e.g. 3 in 2 cells = [1,2], 16 in 2 cells = [7,9]).
Standard
8×8 grids with longer runs requiring cross-referencing of shared factors and digit exclusion pools.
Deep
9×9 grids with complex 5-cell and 6-cell runs demanding global sum parity analysis and digit-pool elimination.
BEYOND+ MASTER EDITIONS
The Master Variants for Kakuro
10×10 Master
Dense 100-cell matrices with interconnected 7-cell runs and cascading sums
A sprawling 10×10 architectural grid with intricate crossing runs and multiple overlapping 6-to-7 cell sum sequences. Requires deep partition mastery and global parity calculations.
- ·Multi-run integer partition lookahead
- ·Cross-intersection constraint propagation
- ·Global board digit parity verification
12×12 Grandmaster
Monumental architectural sum lattices demanding deep partition theory
The ultimate mathematical crossword test across a 12×12 grid. Features exhaustive multi-digit cascades where a single deduction reverberates across ten intersecting runs.
- ·Deep recursive partition deduction trees
- ·Complex multi-sector carryover balancing
- ·Guaranteed single-solution cryptographic validation
FREQUENTLY ASKED QUESTIONS
Questions on Kakuro Architecture
Can digits repeat in Kakuro?
Digits cannot repeat within the same continuous horizontal or vertical sum block, but can repeat elsewhere in the row or column separated by black clue cells.
What is an integer partition in Kakuro?
An integer partition is the unique set of distinct digits 1–9 that sum up to a target number across N cells. For example, a sum of 4 in 2 cells can only be [1,3].
Is there a digital clue helper?
Yes. An unobtrusive integer partition sheet can be accessed quietly without disrupting your focus.
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Play Kakuro on Android
Available directly on Google Play with Gentle, Standard, and Deep tiers included free forever.