Puzzling Asked on March 4, 2021
From TIME to TIME to TIME someone poses a riddle about an inheritance of 17 animals to be distributed to three sons in specified fractions.
My version, complete with an answer, goes like this:
A man died and bequeathed his 17 cows to his 3 sons on the following
plan: the oldest son was to get (1/2) of the cows, the second was to
get (1/3) of the cows, and the youngest son was to get (1/9). The will
did not allow the sons to sell or slaughter the cows or depart from
the specified amounts. The sons wanted to comply with the will but
could see no way to fulfill these terms. What to do?An answer: if there were 18 cows instead of 17, then the oldest
son would take 9 cows, the second son 6 cows, and the third son 2
cows; this is a total of 17, the actual number of cows in the estate.
So take these numbers.
When and where was this riddle first posed? Are there versions of the riddle recorded during the Renaissance? The Middle Ages?
There is an article by one Pierre Ageron entitled "Le partage des dix-sept chameaux et autres exploits arithmétiques attribués à l'imâm ˁAlî. Mouvance et circulation de récits de la tradition musulmane chiite" which, if my French isn't too dodgy, means something like "The division of the seventeen camels and other arithmetical exploits attributed to the imam Ali. Movement and circulation of stories from the Shiite Muslim tradition".
This article is unfortunately not publicly accessible, but here is what purports to be the same article, uploaded to academia.edu by someone purporting to be the author (or at least to share his name).
It says
De même, il ne semble pas que l’histoire des dix-sept chameaux appartienne aux mathématiques arabo-islamiques classiques
("in any case, it doesn't appear that the story of the seventeen camels belongs to classical Arab-Islamic mathematics")
and
Le plus ancien récit de l’histoire des dix-sept chameaux que nous ayons trouvé ne remonte qu’au XVIIIe siècle
("the oldest telling of the story of the seventeen camels that we have found goes back only to the 18th century")
citing one Muhammad Mahdi al-Naraqi of the late 18th century.
(For my part, I have seen several things claiming that the story is much older -- going back "1000 years" or "medieval" or whatever -- but these never provide actual sources of the age they claim.)
Answered by Gareth McCaughan on March 4, 2021
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