HISTORY · 2026-07-25

Kakuro (1966) — From Cross Sums to Addition Cross, Sixty Years of an Unmoved Grid

How a corner feature at Dell Magazines crossed the Pacific, took Nikoli's name, and ended up on Steam's shelves

Introduction — The Other Sibling in Sudoku's Shadow

I have written before about how the magazine Nikoli (1980) raised Sudoku. But the same pages carried another pencil puzzle that never became as famous: Kakuro, also known as Cross Sums. It began in 1966, in a quiet corner of the American puzzle-magazine trade.

Diagonally split black cells carry small clue numbers; white cells are filled with digits 1 through 9, never repeating within a run, so that each run sums to its clue. It looks like a crossword and solves like Sudoku — indeed, Japanese pages of the era often introduced it as 'a cross between crossword and Sudoku.' But this hybrid has its own sixty-year history.

This essay traces that history: from a 1966 Dell Magazines feature, through Nikoli's renaming of it in the 1980s, its re-export to Britain in 2005, and its presence on Steam storefronts today. No single event here is as dramatic as the Sudoku craze, but that is exactly what makes it a good specimen for measuring how durable a puzzle format can be.

Impression of a grid marked with addition symbols (AI-generated)Diagonal clue cells and stacked digits — the primal scene of Kakuro (illustration, AI-generated)

Context — Dell Magazines in 1966, Nikoli in 1983

In 1966, Jacob E. Funk, a Canadian-born employee of Dell Magazines, gave an English name to what would become Kakuro: Cross Sums. Dell was then publishing puzzle magazines by the monthly and quarterly armful — crosswords, Number Place (Sudoku's forerunner), and countless other digit puzzles delivered to American households by mail subscription. This was the golden age of the puzzle magazine as home entertainment, before television saturation and long before home computers.

Cross Sums crossed to Japan only in the 1980s. According to the Japanese Wikipedia, Nikoli mentioned the existence of Cross Sum in a 'coming next issue' notice at the back of Puzzle Communication Nikoli issue 7 (January 1982), but the puzzle itself did not appear that issue. Later that same year, the magazine The Puzzle, from Hagishima Publishing (now Aia), commissioned Nikoli to produce it — the first practical appearance of Cross Sum in Japan, though it drew little attention.

Nikoli itself introduced the puzzle in earnest in August 1983, in the magazine Monthly Nikolist. It translated 'Sum' into Japanese as 'kasan kurosu' (addition cross), later shortened to Kakuro. At almost the same moment, Nikoli was also renaming the American-born Number Place into Sudoku. Kakuro and Sudoku are, in this sense, two children raised by the same foster parent.

Impression of a 1960s American mail-order puzzle magazine and 1980s Japanese pages (AI-generated)Pages from the mail-subscription era, and a renaming story that crossed the Pacific (illustration, AI-generated)

Mechanics — One Rule Against Repetition, and the Combinatorics It Creates

Kakuro's rule is simple. Each run of white cells (a contiguous horizontal or vertical stretch) must be filled with digits 1 through 9 that sum to the clue assigned to that run, without repeating any digit within the run. This single constraint against repetition is what makes a unique solution possible. A two-cell run summing to 3, for instance, can only be 1 and 2; a sum of 17 can only be 8 and 9. Memorizing this table of uniquely-determined combinations is the first step to solving Kakuro.

The difference from Sudoku is that the given clues are sums, not digits themselves. Solvers narrow down candidate combinations for intersecting runs and isolate shared digits by elimination. Japanese computer scientists Takayuki Yato and Takahiro Seta, in papers from 2003–2004, showed that this class of puzzle is NP-complete. It is easy to underestimate by hand, but mathematically Kakuro sits among the harder puzzle types.

What's notable is how this 'work backward from a sum' idea lets two separate lineages share one board: the crossword's grid design (put to paper in 1913) and Sudoku's digit-filling logic. Kakuro was never meant as an arithmetic drill; it trained the mental arithmetic of countless readers as a lesson in combinatorics, tucked in the corner of a magazine page.

Impression of a logical structure working backward from sums (AI-generated)Two crossing runs, combinations narrowing down — the logical skeleton of Kakuro (illustration, AI-generated)

Legacy — Re-Export, the DS, and a Shelf Still Standing on Steam

Kakuro became internationally known just after the global Sudoku boom of 2004–2005. According to the Japanese Wikipedia, once Nikoli began supplying puzzles to The Guardian in 2005, the Japanese-derived name 'Kakuro' spread widely in the English-speaking world; the English Wikipedia cites The Guardian's own feature, 'The New Grid on the Block,' as a primary record of that spread. Cross Sums, born in America in 1966, had been renamed in Japan and was now coming home again as 'Kakuro.' 'Kakkuro' and 'KAKURO' remain registered trademarks of Nikoli to this day.

The move from paper to digital screens came early. On August 10, 2006, Hudson released Puzzle Series Vol. 4: Kakuro for the Nintendo DS, with Nikoli credited for puzzle supervision. It offered grids from 5×5 up to 13×21 and a hint feature that listed unique-sum decomposition patterns — the same wave of portable Sudoku conversions carried Kakuro from paper to handheld screens.

And today, in 2026, a look at Steam's storefront turns up standalone titles still selling: Kakuro, Kakuro Blend, Kakuro++, Super Kakuro - Cross Sums. Devised in 1966, renamed in 1980s Japan, re-exported to a British newspaper in 2005, ported to a handheld in 2006 — this grid has spent sixty years changing containers without changing a single rule. Few puzzle formats survive that long, unaltered.

Impression of a lineage running from paper magazines through the Nintendo DS to today's digital storefronts (AI-generated)From mail-order magazine to handheld to storefront — an unchanged grid in ever-changing containers (illustration, AI-generated)

Sources

Sources consulted for this article:

Wikipedia: Kakuro

Japanese Wikipedia: Kakkuro (カックロ)

The Guardian: The New Grid on the Block

Nikoli: Kakuro (official)

MobyGames: Puzzle Series Vol. 4: Kakuro (2006)

Wikipedia: Puzzle Series (Hudson)

Berthier, D. (2013). Pattern-Based Constraint Satisfaction and Logic Puzzles. arXiv:1304.1628

Yato, T. & Seta, T. (2003). Complexity and Completeness of Finding Another Solution and Its Application to Puzzles. IEICE Transactions E86-A(5)

Steam: Kakuro

Steam: Kakuro

Steam: Kakuro Blend

Steam: Super Kakuro - Cross Sums

Closing — A Rule That Survives Any Container

What Kakuro's history shows is not a dramatic invention story or a viral craze. It is the fact that a single constraint — no repeated digits — survived sixty years of container changes, from mail-order magazines to the Nintendo DS to Steam storefronts, without breaking. It never triggered a global frenzy the way Sudoku did, and that is precisely what makes this modest grid of sums a good ruler for measuring the sheer durability of a rule.

The design aesthetic that today's indie puzzle scene likes to praise — a vast possibility space unfolding from a minimal rule set — is something Kakuro was already embodying back in 1966. Two constraints, a sum and a ban on repetition, are enough to make every board tell a different story of deduction. As a historian, I can offer one claim with confidence: a good puzzle rule outlives the media that carry it.

Impression of a quietly completed grid (AI-generated)A pencil set down beside a just-finished square (illustration, AI-generated)

Reactions (no login)

Anonymous • one of each per visitor per day

関連シリーズ

Puzzle Incident History第14回 / 全14回

次に読む