## Sudoku's French ancestors

Everything about Sudoku that doesn't fit in one of the other sections

### Sudoku's French ancestors

I have been in correspondence with Christian Boyer from France. He has recently written an article for "Pour La Science" (the French eidition of "Scientific American") on the subject of Sudoku's history.

We know about Euler's involvement with Latin Squares, dating to his paper of 1782. We know that the first known appearance of a Sudoku puzzle in the USA was in 1979. Did nothing happen between 1782 and 1979?

It is sometimes claimed, on the strength of the 1979 first known appearance, that the puzzle was invented then. However, the first known appearance of something is not proof of the time of its invention. It certainly constitutes circumstantial evidence of the time of invention, but it is not proof in itself. Perhaps I am influenced in this by my years as a Judge.

Christian Boyer has uncovered a series of puzzles which appeared in French newspapers in the 1890s. French dailies and magazines published a variety of games that featured the ingredients of Sudoku, such as:
* 9x9 grid with 3x3 boxes;
* blanks to fill with numbers;
* the digits 1 through 9 in each row, column and even box.

Not all of those ingredients come together in every puzzle, and they shared the Daily Puzzle slot with other kinds of puzzles. However, Christian illustrates some remarkable puzzles, including one (dating to July 6, 1895) which -
* if solved like a Sudoku puzzle produces 2 solutions;
* but which if solved with the setter's additional rule that the broken diagonals must add up to 45, produces 1 solution.

The way the puzzle was printed at the time, it did not have the 3x3 boxes appearing with heavy outlines. It seems the setter was approaching it more as a magic square than anything else. However, coincidentally or not, the puzzle does comply with the basic Sudoku rules, including the requirement that each 3x3 box contain the digits 1 through 9. However, the single correct solution does allow repetition of the digits in broken diagonals.

Christian's research may have uncovered the "missing link" - or at least one of the missing links - between Euler and Sudoku.

You can find Pour La Science at www.pourlascience.com

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

It is mathematically and historically obvious, that sudokus must have been invented long before 1979.
The puzzle is simple, rich, and beautiful.
But , with no computers, it´s hard to make them popular. Moreover , popularity depends more on mass-media than on the brilliance of the puzzle.
Though sudokus, because simple (simple rules, but hard to solve), are brilliant.

We are glad to share with judges and architects our love for logic
and maths.

The simplest puzzle is always the best, and sometimes the harder.

Posts: 23
Joined: 22 May 2006

Christian Boyer has written to me as follows:
You say “However, the single correct solution does allow repetition of the digits in broken diagonals.” You perhaps know that such a solution is impossible for any 9x9 sudoku. A 9x9 sudoku can’t have all its broken diagonals using all digits 1 to 9. The smallest possible sudokus with correct broken diagonals are 25x25. More details at www.multimagie.com/English/SudokuPandiag.htm, look at my letter published in Mathematics Today.

For more information about these early French puzzles, take a look at www.multimagie.com/indexengl.htm, because a supplement of the Pour La Science article can be downloaded, with some pictures of these old puzzles: from the welcome page, click on “ici supplément à télécharger”.

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

Here's an updated reference to the English-language version of the relevant article/s:
www.multimagie.com/English/SudokuAncestors.htm

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

### Christian Boyer

Euler was not french he come from Switzerland!
Papy
Papy

Posts: 131
Joined: 15 August 2006

I am happy to announce that an English version of my article is published in the current issue of The Mathematical Intelligencer, Vol. 29, N. 1, 2007, pages 37-44.
This article titled “Sudoku’s French Ancestors” is a revised and enhanced version of the original French article “Les ancêtres français du Sudoku” published in Pour La Science.

Try to solve the nine old problems of the article!!!
9x9 grids to fill in with numbers, several of them with 3x3 boxes, published in French newspapers at the end of the 19th century.
Their solutions will appear in the next issue of The Mathematical Intelligencer.

Christian Boyer.
www.multimagie.com/indexengl.htm

PS to Papy: Euler was not French, of course. Who said that?
cboyer

Posts: 1
Joined: 20 May 2007

But , with no computers, it´s hard to make them popular

It isn't as hard as it seems to make puzzles by hand, although computers do make it easier to check dificulty levels etc.
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Pi

Posts: 389
Joined: 27 May 2005