Subject: Re: [HM] Towers of Hanoi
From: David Singmaster (david.singmaster@sbu.ac.uk)
Date: Fri Feb 11 2000 - 07:38:25 EST
I can confirm Cabillon's assertions.
I received photocopies of the material in the Conservatoire National
des Arts et Metiers about two years ago. This included descriptions of
two examples presented by Lucas in 1888 (one 'grand mode\le pour les cours
publics', 1.05m high!), the cover of an original box, the original
instructions of 1883 which already give the Be/nare\s story and offer
a prize of a million (= US billion) francs for a demonstration of the
complete solution (incidentally Robert Ripley was taken in by this and
included it in one of his early Believe It or Not books), and of two
inscriptions on the boxes, as follows.
Hommage del'auteur Ed Lucas Paris 1888 (The date is not fully
legible on my copy but could be 1888 which is the date he presented the
item.)
Inside the cover, in the same hand, is:
La tour d'Hanoi", --
Jeu de combinison pour
expliquer le systeme de la nume/ration
binaire, invente/ par M. _Edouard Lucas_,
(novembre 1883. -- donne/ par l'auteur.
(In the above, I use /, \, ", to denote accent acute, accent
grave and umlaut (or dieresis) on the previous letter. Material
between _ _ is underlined.)
As far as we know, this is the only place where Lucas explicitly
stated that he invented the puzzle, but it seems to have been common
knowledge as the anagrams are decoded in article already in 1883.
The earliest known articles are the following.
G. de Longchamps. Varie/te/s. J. de Math. Spe/ciales (2) 2
(1883) 286-287. (This is only signed G. L., but the author is
identified in the index on p. 290. Andreas Hinz found this and sent
me a copy.) He refers to a letter from 'professor N. Claus'. He
solves the recurrence for the number of moves.
Henri de Parville. Column: Revue des sciences. J. des De/bats
Politiques et Litte/raires (27 Dec 1883) 1-2. Gives the Benares
story. He already notes the anagrams.
N. Claus (de Siam). La tour d'Hanoi". Jeu de calcul. Science et
Nature 1:8 (19 Jan 1884) 127-128. This cites Longchamps for the
number of moves, though I originally thought it might be a fictitious
reference! This mentions that each of the discs always moves in the
same direction which gives the standard solution, which is attributed
to the nephew of the inventor, M. Raoul Olive, a student at the Lyce/e
Charlemagne. Asks for the minimum number of moves to restore an
arbitrary legal arrangement of discs to a Start position, but says
this is complex and refers to Lucas' Re/cre/ations mathe/matiques of
1884 for binary arithmetic.
In later writings, there are several references to the following by
Lucas.
Jeux scientifiques pour servir a\ l'histoire, a\ l'enseignement et
a\ la pratique du calcul et du dessin. 1889. These are described as
a series of six brochures, but may have been booklets for the actual
games invented by Lucas and marketed. One of these, for La
Pipopipette (= Dots and Boxes), is reproduced in L'Arithmetique
Amusante, but I have not seen any of the others. Andreas Hinz has
found some of them, but not the one for the Tower of Hanoi. If
anyone finds any of these, I'd be delighted to have a copy.
David Singmaster
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