Suirodoku is a published mathematical object: a proven minimum of 13 clues, versus 17 for classical sudoku.
Latin & Graeco-Latin square
The figure that explains it all
Latin square
one symbol, once per row and column
Graeco-Latin square
two symbols, each pair unique
A Latin square arranges symbols so each appears exactly once per row and column (on the left: A, B, C, D). Overlaying two of them — Latin and Greek letters — so that each pair (Aα, Bβ…) is also unique gives a Graeco-Latin square. We owe these objects to the mathematician Euler (1782): his Latin and then Greek letters actually gave the two squares their names. Tsuidoku is exactly that, but 9×9 with digits and colors — plus the sudoku’s 3×3 blocks.
Other famous squares
The Sator square — the oldest known word square (found at Pompeii, before 79 AD). It reads the same both ways (a palindrome). Its letters repeat, so it is not a Latin square, but it is the most famous of all squares.
The Lo Shu square — the oldest known magic square (China, over 2,000 years ago). Every row, column and both diagonals sum to the same value: 15. Another way to order a square — by sums, not by uniqueness.
Dürer’s magic square — engraved in Melencolia I (1514). Rows, columns and diagonals all sum to 34; the two bottom cells, 15 and 14, spell the year of the work. Art and mathematics in a single grid.
The names, in Japanese
su
number
iro
color
tsui
pair
doku
single
SUDOKU
classic sudoku · number + single
SUIRODOKU
the color version · insert “iro”
TSUIDOKU
the app’s name · “tsui” = pair
Sudoku comes from the Japanese 数独: 数 (su) means number and 独 (doku) means single — each digit stays single, once per row, column and block.
The colored version renames the game around its extra layer. Suirodoku inserts 色 (iro, color): Su-iro-doku, the color sudoku. Tsuidoku uses 対 (tsui, pair) for the 81 unique digit-color pairs at the heart of the grid — written 対独.
Two mathematical worlds
A two-century bridge
Tsuidoku sits at the crossroads of two areas that long remained strangers to each other: sudoku, a recent one, and another far older, more than two centuries old. Having never spoken to each other, each coined its own vocabulary.
The sudoku side (2000s)
Recent, it deals with the grid of numbers and its constraints: the total number of possible grids, the smallest number of clues that guarantees a unique solution (17 in classic sudoku), and solving by logical deduction. It counts the grids that are « essentially different » once symmetries are set aside — swapping bands, stacks, rotations.
The Graeco-Latin side (Euler, 1782)
Far older: it all starts with the 36 officers problem posed by Euler in 1782 — arranging 36 officers of 6 ranks and 6 regiments so that every row and column brings them all together. Superimposing two grids so that each pair appears only once is exactly what the numbers and colours of Tsuidoku achieve. This field groups equivalent grids into « orbits » and sorts them into large families, the « species ».
In essence, a Tsuidoku is a Graeco-Latin square with the sudoku constraints added on top: the 3×3 blocks. It is that double rule that makes it an object of its own.
How many are there? Nobody knows yet. But their number already far exceeds that of sudokus: a single grid of numbers can be completed with billions of different colour grids. The whole is far vaster and richer than sudoku alone.
Where Tsuidoku fits
At the intersection of two families
Latin square
unique row & column
↓
Sudoku
+ 3×3 blocks
Graeco-Latin square
+ unique pairs
↓
Tsuidoku
blocks + unique pairs
A Latin square yields two traditions: sudoku (which adds the 3×3 blocks) and the Graeco-Latin square (which adds unique pairs). Tsuidoku is both at once.
The history, in dates
From Euler to Tsuidoku
1782
Euler poses the 36 officers problem — 6 ranks, 6 regiments, impossible to arrange.
1900
Tarry proves that no solution exists for order 6.
1959
Bose, Shrikhande & Parker disprove Euler: Graeco-Latin squares exist for every order ≥ 10.
1979
Howard Garns invents modern sudoku in the United States, under the name Number Place.
1984
Publisher Nikoli releases it in Japan and names it 数独 (sūdoku) — “single number”.
2004
Wayne Gould gets it into The Times of London: sudoku becomes a worldwide phenomenon.
McGuire proves sudoku’s minimum of 17 clues — 800 processor-years of computation.
2026
Jordan Maire, creator of Tsuidoku, proves the minimum of 13 clues and discovers the Crystal Grid, the most symmetric grid.
?
And how many Tsuidoku grids exist? The exact count is still unknown — research continues.
The most symmetric grid
The Crystal Grid
The most symmetric Tsuidoku of all (1,296 symmetries, an absolute record), discovered by Jordan Maire in 2026. Its digit layer and color layer are interchangeable: swapping the two yields the same grid.
Wild facts
6 records & curiosities
1
The most symmetric sudoku in the world is called the back-circulant: 648 symmetries, the absolute record. In 2012, only 9 color mates able to form a Tsuidoku were known for it. The exact enumeration of 2026 reveals 3,622,317,453.
2
Hidden among those 3.62 billion is the Crystal Grid, discovered in 2026: the most symmetric Tsuidoku of all. Its digit layer is the back-circulant; its color layer is the unique mate preserving its 648 symmetries, and since swapping digits and colors gives back the same grid, its symmetry doubles: 1,296. The flip side: too much symmetry dilutes information, and its puzzles only have a unique solution from 27 clues up, the highest value observed.
3
No classical sudoku in the world has a symmetry of order 81: it is algebraically impossible. Adding the color layer lifts the ban: a Tsuidoku grid discovered in 2026 realizes this symmetry, out of reach for sudoku alone.
4
In 4×4 miniature, everything can be counted exactly: there are 288 sudokus, and each admits on average exactly 8 valid colorings, for 2,304 Tsuidoku in total, eight times more than sudokus.
5
Every Tsuidoku generates 'mutually unbiased' quantum bases in dimension 81, an unexpected bridge to quantum cryptography.
6
Colors and numbers don’t run on the same brain circuits. A color is spotted “in parallel,” almost instantly, by area V4 of the visual cortex; a digit is a symbol the brain decodes more slowly, drawing on the intraparietal sulcus, the seat of the number sense — two networks, two modes of attention. Yet Tsuidoku forces you to deduce a color from a digit, and the reverse: in every cell you make these two normally-independent systems talk to each other. That back-and-forth engages exactly the kind of cross-network integration from which new connections arise — “neurons that fire together wire together.”
What it looks like
A 13-clue example
Example — just 13 clues lock an entire grid, versus 17 minimum in classic sudoku: since each cell carries two pieces of information (digit + color), each clue says twice as much.
The proofs
Three published papers
Research, proofs and writing: Jordan Maire, creator of Tsuidoku.
The 13-clue theorem
Solving a classical sudoku requires at least 17 clues, a result that cost 800 processor-years of computation (McGuire, 2014).
The founding paper proves a Bijection Theorem: each digit-color pair exists exactly once in the grid, every cell has an absolute identity, impossible in classical sudoku.