Pour La Science, n°346, August 2006, Readers' letters column.
Letter from Michel Feuillée on the "Sudoku's French ancestors" article.

Sudoku's new ancestor

Further to the article Sudoku's French ancestors (Pour La Science, n°344, june 2006), I point out an article published in La Nature magazine, December 26 1885. In a 4x4 square, "place the Aces, Kings, Queens, Jacks of a pack of cards with (in each row, column and diagonal) one and only one card of the same value, and one and only one card of the same suit". It has to be compared with the 81 officers problem of the article, because each element has two attributes.

Is it possible to construct a 16x16 sudoku, with sixteen 4x4 subsquares with these cards and with the above rules for each 4x4 subsquare, but with each row or column of 16 cells containing the 16 cards, that is to say the 4 honors (Aces, Kings, Queens, Jacks) in the 4 suits (club, diamond, heart, spade)?

Michel Feuillée, Franconville la Garenne, France

Christian Boyer's answer

Your problem of 1885 confirms the big interest of the French at that period in these questions. Its solution can be found through an Eulerian magic square. Here is one of the numerous possibilities. You will notice that it is also a stacking of two 4x4 sudokus, each 2x2 subsquare including also all the cards :

The problem you have added is much more difficult. Even though 16x16 are known, and even though 4x4 Eulerian squares are well known, your mixing of the two questions seems new. Here is a solution:

The most difficult was to get all the diagonals of the 4x4 subsquares correct (with the four honors and the four suits of cards). You will recognize in the upper left corner the previous solution of the 1885 problem. I let you convert in base 4 and in playing cards, with the same conversion rules.

Christian Boyer

La Nature's articles

After the publication of this column, Michel Feuillée sent me the solutions of the 4x4 problem as they were published in La Nature 1885 and 1886. His new 16x16 problem was of course not present.

La Nature, Dec 26th 1885 page 63, and June 19th 1886 pages 42-43
(click on images to enlarge them)

Thanks to Michel Feuillée.

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