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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?

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  • $\begingroup$ I have seen versions on the internet dating back to 2009, but I really don't know the answer to this. $\endgroup$ – Quintec Feb 9 '18 at 16:12
  • $\begingroup$ Since it has to do with Mathematics and animals, so probably some scholar thought about it while working on number theory. $\endgroup$ – ABcDexter Feb 9 '18 at 17:09
  • $\begingroup$ I posted a bunch of comments here, which I'm about to delete because I've turned them into an answer. $\endgroup$ – Gareth McCaughan Feb 9 '18 at 18:01
  • $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) $\endgroup$ – Rubio Mar 3 '18 at 9:02
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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.)

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    $\begingroup$ Great find. The oldest one I knew was 1893, Professor Hoffman's Puzzles Old & New, which is mentioned in passing the paper. This is a seminal puzzle book still being reprinted today, though it can't have been the one to popularise the puzzle in the West since it changes it to be about an old farmer leaving horses to his sons. $\endgroup$ – Jaap Scherphuis Feb 10 '18 at 7:39
  • $\begingroup$ A lot of the western versions of this puzzle I've seen do have horses or sheep rather than camels, so I don't think you can rule out the possibility that it went camels -> horses -> camels :-). $\endgroup$ – Gareth McCaughan Feb 10 '18 at 12:32
  • $\begingroup$ FWIW, the oldest I'd seen before trying to answer this question was 1931 (Dudeney's "Puzzles & Curious Problems"). That has horses too. $\endgroup$ – Gareth McCaughan Feb 10 '18 at 12:36
  • $\begingroup$ This article also speculates, from a much later source: « la version soufie [...] a [...] pour but [...] de permettre et accompagner un franchissement d’étape dans l’initiation.On peut émettre l’hypothèse que l’histoire des dix-sept chameaux aurait son origine dans les cercles soufis, où elle aurait rempli une fonction de ce type. Elle aurait ensuite été « chiitifiée » en Iran au XVIIIe siècle.», that is “The sufi version’s goal is [...] to allow and support the crossing of a step in the intiation. One can hypothesize that the 17 camels story had its origins in sufi groups, where it had ...” $\endgroup$ – Frédéric Grosshans Mar 29 '18 at 13:31
  • $\begingroup$ “... such a function. She would then have been «shiitified» in Iran driting the 18th century”. «Shiitified» correspods to a French neologism, meaning “rendered shiite”, since the 18th century Iranian version gives a proeminent role to Ali, a key personage of shia Ialam $\endgroup$ – Frédéric Grosshans Mar 29 '18 at 13:35

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