**Sudoku's French ancestors**

*
"Les ancêtres français du sudoku", Pour
La Science, June 2006, pages 8-11 & 89.*

For a summary of the article, read below the English version of the press
release sent by *Pour La Science* to the English-speaking press. You
can also read texts or comments on the article from:

**Wayne Gould**, who successfully popularized sudoku puzzles in the world, in his website http://www.sudoku.com/forums/viewtopic.php?t=4228**Brian Hayes**, author of the "Computing Science" column in*American Scientist*, in his website http://bit-player.org/2006/sudoku-dans-la-belle-epoque**Jack Malvern**, in his article published in*The Times*, June 3 2006, http://www.timesonline.co.uk/article/0,,2-2208881.html (unfortunately with an error)**Caroline de Malet**, in his article (in French) published in*Le Figaro*, June 26 2006, http://lefigaro.fr/sciences/...

At the end of my article, page 11, I mentionned some
downloadable supplements. They are available both on the *Pour
La Science*'s
website and here:

- Download the supplement (in French) to the article (PDF file, 781Kb)
- Download the solutions (in French) of the supplement (PDF file, 372Kb)

In these PDF files, you will find some other French old problems,
some photos of the French old newspapers, and my difficult sudoku
puzzle reported by **Jean-Paul Delahaye** in *Pour La
Science*, January 2006, page 9. As described in the downloadable solutions, only
one reader successfully solved this last problem: **Louis Caya**, Canada.
Congratulations to Louis!

See also the page on the relationship between sudokus and bimagic squares (page written in December 2005, before the article).

*"Sudoku's
French Ancestors", The Mathematical Intelligencer, Vol. 29, N.1, Winter
2007, pages 37-44 "Sudoku's
French Ancestors - Solutions to the Problems", The Mathematical Intelligencer,
Vol. 29, N. 2, Spring 2007, pages 59-63*

There is a English, revised, and enhanced version of the article initially
published in French in *Pour La Science*: this new version titled
"Sudoku's French Ancestors" was published in *The Mathematical Intelligencer*
in two issues of 2007. Thanks to **Chandler Davis** (editor-in-chief of the
M.I.) for his English translation, and thanks to **Michael Kleber** and **Ravi
Vakil** (editors of the "Mathematical Entertainments" column of the
M.I.).

In the August 2006 issue of *Pour
La Science*, page 29, I answered to two interesting
problems asked by **Michel Feuillée**
after my June article.

Unfortunately my answer to the second problem, a 16x16
sudoku, was published *without* the 4x4 borders: a sudoku without
the borders of its subsquares is so difficult to analyze! See
the Feuillée's question and my answers, this time *with* the bordered
subsquares. And with copies of the articles published in *La Nature* in
1885-1886.

**Press Release**

Up until now the sudoku was considered a recent game.
Here is a forgotten fact, revealed by **Christian Boyer** in the
June 2006 issue of *Pour La Science*:
in the 1890’s, one century before the sudoku, the French used to complete
sudoku-like grids which were published in major daily newspapers.

**---- History as we’ve known it until now**

Since 2005, sudoku grids have enjoyed worldwide success. They are a fascinating game, and once one gets started on a grid, it is very difficult to put it down before solving it…

The story of the sudoku has often been told. The first sudokus were published
in 1979 by the American **Howard Garns**. They then appeared in Japanese
magazines in the 80’s and 90’s, where they took their current name. Their
international success really started thanks to New-Zealander **Wayne Gould**,
who published them in *The Times* of London starting in November 2004.
The *Daily Mail*, the *Daily Telegraph*, and many other dailies and
magazines all around the world followed suite. An incredible success!

Long before this, Swiss mathematician **Leonhard Euler** had invented
Latin squares in his study published in 1782 and written in French : « Recherche
sur une nouvelle espèce de quarrés magiques » (Research on a new species of
magic squares). Even though sudokus are based on Latin squares, Euler hadn’t
thought of the sudoku 3x3 sub-squares, and also hadn’t emphasized the playful
aspect of his invention of not letting readers guess missing numbers.

**Figure
1**. This very simple 9x9 Latin square published by
Euler in 1782

is not made up of sudokus 3x3 sub-squares.

An nxn Latin
square is a square that features all the whole numbers found

between 1 and
n in each line and each column.

**---- History revealed in Pour La Science**

Did nothing happen between 1782 and 1979? The *Pour La Science* article
reveals that at the end of the 19th century, French dailies and magazines published
a variety of games that featured all the ingredients of a sudoku:

- 9x9 grids with 3x3 sub-squares
- blanks to fill in with numbers
- and even for some, the single use of numbers from 1 to 9 in each line, column, or even sub-square

**Figure
2**. One of the numerous 9x9 with 3x3 sub-squares problems

published
in the late 1800s. This one was published in Le Siècle in 1892.

These characteristics appeared gradually, in problems published in dailies
like *Le Siècle*, *La France*, *Gil Blas*, l’*Echo de Paris*,
or in magazines like *Les Tablettes du Chercheur*, *La Revue des Jeux*.

The most sudoku-like grid that **Christian Boyer** found is one by **B.
Meyniel**, published in the daily *La France*, dated July 6, 1895. It
is shown here in figure 3, with the sub-squares borders added. At the time,
this 3x3 sub-squares structure was directly highlighted in numerous other problems,
like the one in figure 2, published in 1892.

**Figure
3**. Grid published by B. Meyniel in 1895. Can you solve
it?

Both diagonals must also include all the numbers between 1 and 9.

If
you solve it like a sudoku, this problem has 2 solutions.

But there is only
one way to solve it if you follow with the author’s rules:

all the broken
diagonals (like the one on a blue background) must total 45.

In the June issue of *Pour La Science*, you will find other French problems
from the past, forgotten for over a century - ancestors of the sudoku. And their
solutions!

**----------------**

*Pour
La Science* is the French edition of

In 2003, **Christian Boyer**
and **Walter Trump**, were the
first to solve the old problem of the smallest perfect
magic cube. This problem, popularized by **Martin
Gardner** in *Scientific American*
in 1976, had initially been studied by **Pierre de Fermat**
as early as 1640.

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