Talk:Propositiones ad Acuendos Juvenes

Dead external link

The 3rd and last external link seems to be dead, does someone know a working link? TeunSpaans (talk) 18:01, 16 August 2011 (UTC)

[1]. Spacepotato (talk) 22:49, 17 August 2011 (UTC)

Pigs problem (Problem 43)

For the pigs problem, why not try any 2 odd numbers then zero. E.g. 151, 149 , 0 . Since no number of pigs got slaughtered the 3rd day, it doesn't violate the rule. 70.54.202.152 (talk) 15:30, 14 November 2012 (UTC)

0 is not an odd number. 138.16.21.199 (talk) 02:57, 27 January 2013 (UTC)

In English, one could equivocate on the subtle differences between "kill" and "slaughter" -- the latter is more typically used to mean cutting up an animal for meat. So one could drown one of the pigs minutes before the start of the first day, but wait until the start of the first day to slaughter it. Would that work in the original Latin ("Homo quidam habuit ccc porcos, et jussit, ut tot porci numero impari in iii dies occidi deberent.")? Unfortuately, I don't know Latin. KevinBTheobald (talk) 01:28, 23 March 2020 (UTC)

Basic parity says there's no way to do this that doesn't rely on some sort of trick, obviously. Two possibilities suggest themselves: 1) a variant on the old "dividing up the flock between the sons" puzzle - add another pig and slaughter that as well. Or 2) slaughter one pig across a midnight, so that it counts towards two days. Both somewhat tenuous, though.77.99.23.170 (talk) 20:50, 31 May 2021 (UTC)

Prob five incorrect?

I do not get what the question is in that one. Is there something missing? --129.13.72.198 (talk) 20:47, 21 April 2013 (UTC)

Ah. A couple of course can also mean a pair, two. --129.13.72.198 (talk) 20:52, 21 April 2013 (UTC)

One way to solve using modern methods is to express it as two equations in three unknowns. Obviously this is underspecified, but eliminating the number of piglets reduces this to one equation in two unknowns, and the fact that the solution has to be two non-negative integers makes simple enumeration trivial. (Can any math historians out there say whether these techniques were known by Alcuin or his audience? Had the Arabic translations of the works on Diophantine equations made their way back to Europe by then?) KevinBTheobald (talk) 06:07, 25 February 2019 (UTC)

Going through a translation I found online (and cited in the article), I found six other problems nearly identical in form to #5. In most cases, using Gaussian elimination to remove one unknown leads to an equation with a fraction containing a large prime number, such as 71. This forces the numerator to be the same, leading to the solution directly without enumeration. KevinBTheobald (talk) 21:42, 6 January 2020 (UTC)

Full list of puzels...?

While it may not be easy to find a full list which is in public domain, then we may be able to get a summary -- http://www-gap.dcs.st-and.ac.uk/history/PrintHT/Alcuin_book.html -- is from a uk university, and may be suitable source. 99.103.198.159 (talk) 11:05, 10 August 2014 (UTC)

Problem 42

Does the cited reference explicitly claim that Gauss's solution is "more elegant"? Elegance is in the eye of the beholder. While Gauss's solution is mathematically more direct, Alcuin's might be easier for children (the intended readers) to grasp, especially in his time, which preceded use of decimal numbers in Europe. KevinBTheobald (talk) 05:54, 25 February 2019 (UTC)