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Topic: [HM] Fleury's algorithm
Replies: 6   Last Post: Nov 28, 2004 5:33 PM

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David Singmaster

Posts: 1
Registered: 1/30/05
Re: [HM] Fleury's algorithm
Posted: Nov 28, 2004 5:33 PM
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On 16 Apr 2002, Margherita Barile wrote some information about Fleury
and his algorithm, and on 1 Jan 2003, Adam Drozdek provided a
Barile says "Edouard Lucas, in his book "Recreations Mathematiques"
(appeared for the first time in Paris in 1891), refers to a certain
"M. Fleury" as a "chief of institution" from Marseille who published
his algorithm in the note "Deux problemes de geometrie de situation",
published in a 1885 issue of the French periodical "Journal de
mathematiques Elementaires". He gives page 257 as a reference. I,
however, could not find this page."
I have done a little searching and I have a number of comments.
Lucas's book has four volumes. Vol. 1 appeared in 1883, with a 2nd
ed. in 1891. Vol. 2 appeared in 1883 with a second edition in
1893(?). Vols. 3 & 4 appeared in 1893 & 1894, and never had second
editions. The currently available reprint series uses the 2nd ed. of
vol. 1 and the 1st ed. of vol. 2. I have never observed any
significant differences in the editions of vol. 2, but I have not seen
a copy of the 1st ed. of vol. 1.
Lucas's books (like all too many 19C works) are notorious for not
having indexes. Consequently a reference without a volume and page is
a real pain to try to track down, especially for a topic like Fleury's
algorithm which might occur in a number of different places.
So far as I can tell, Fleury is not mentioned in the 2nd ed. of vol.
1, EXCEPT that his paper Deux proble\mes de Ge/ome/trie de situation
in Journal de Math. e/le/m. is listed on p. 247, but with year 1885,
which Drozdek corrects to 1883. [e/ is e with an accent acute; e\
is e with accent grave.]
Fleury is cited extensively in vol. 4, pp. 240-254, which describes
him as the inventor of a number of games, some of which were
previously described in vol. 3, pp. 87-103, but he is not mentioned
None of the references above say that Fleury was a "chief of
institution" from Marseille.
For material of this period, one of the best sources is Wilhelm
Ahrens' Mathematische Unterhaltungen und Spiele, 2 vols., 2nd ed.
1910, 1918 (publication was interrupted by WW1; there is a 1921 3rd ed
of vol. 1, but it has only some corrections made and 2pp of extra
notes). He has a bibliography of 762 items and a thorough index which
cites Fleury twice and two of his papers (a misprint cites another
In vol. 2, p. 231, in a long footnote on the Fifteen Puzzle, Ahrens
cites an 1880 paper of Fleury (no. 374 in his bibliography), which he
has not seen.
In vol. 2, p. 239, in a footnote on the question of parity in the
Fifteen Puzzle, Ahrens notes that the use of two identical pieces
makes all positions solvable, as in the variant French game invented
by Fleury and named Came/le/on. Ahrens refers to Lucas, vol. 3, pp.
89-99, 155-158 (I don't see anything relevant on the latter pages, but
perhaps this was another of Fleury's games), to vol. 4, pp. 240-254
and to two papers of Fleury in Interme/diaire des mathe/maticiens, 1
(1894) 215-216 (cf p. 35) [item 524 in the bibliography] and 5 (1898)
159-160 (cf p. 28). Not having seen these, I'm not quite sure why he
has added the cfs.
In vol. 2, p. 403 has the bibliographic item 374: Fleury, H. "La
cle/ du taquin, ou la solution des quinze." Marseille, 1880.
In vol. 2, p. 414 has the item 524: Fleury, Henry. [U"ber das
"Chama"leon" und verwandte Spiele.] Interme/d. des mathe/m. 1, 1894,
p. 215-216. [Here U" denotes U with an umlaut and a" denotes a
with an umlaut.]

Hope this is of some use.
David Singmaster

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