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“Do not give your books to children!” and other medieval tips for taking care of books

Gashed gatherings, bodged bindings and faltering flyleaves. The current state of medieval manuscripts, either good or bad, reflects the manner in which manuscripts have been retained and used over the centuries. Nowadays, the concern over the preservation of books leads to ever stricter regulations on access, handling and storage. But what about the Middle Ages? Did contemporary makers or users of books set any rules on how to treat these objects? This blog post calls attention to a late medieval Middle Dutch text which provides guidelines as to how to preserve books ‘to last forever’ -some of these rules remain topical today!

Caring for books in the Middle Ages

Medieval, written sources on the care of books are relatively scarce. An interesting case is the  Philobiblon, written by Richard de Bury (1287-1345). In this work of passionate bibliophilia, Richard expresses his profound love for books. He also shows an awareness of the dangers that threaten a book’s well-being. Not least of all, Richard laments the maltreatment of manuscripts by snotty youths, who, rather than wipe their noses, stain their books:

You may happen to see some headstrong youth lazily lounging over his studies, and when the winter’s frost is sharp, his nose running from the nipping cold drips down, nor does he think of wiping it with his pocket-handkerchief until he has bedewed the book before him with the ugly moisture. Would that he had before him no book, but a cobbler’s apron! (De Bury, ch. 17)

In monastic libraries, some measures were taken to prevent damage to books. Most monasteries appointed a so-called armarius, a librarian avant la lettre, who was responsible for managing and preservation of the manuscripts (Clark 1902: 57).  According to the fifteenth-century monastic rules of the St. Paul’s house for the Brethren of the Common Life in Gouda, the armarius was also supposed to take into account the dangers posed by bookworms and dust (Lem 1991). Other monasteries add dirt, and damage caused by humidity and/or fire to these instructions (Clark 1902: 61). None of these monastic rules provide any practical advice, however, as to how these risks could be minimised.

‘How one shall preserve all books to last eternally’

Specific rules and practical advice on book conservation is provided by the author of the text entitled ‘Hoemen alle boucken bewaren sal om eewelic te duerene’ [How one shall preserve all books to last eternally]. This unique text, in the Dutch vernacular, outlines eight rules on access, handling and storage. The text is found in The Hague, KB 133 F 2: a miscellany on 180 folia of 120x79cm, written entirely by one hand. Various ownership inscriptions, in the hand of the main text, suggest this book was made in 1527 and that it belonged to ‘Margrieten van der Spurt’ from Ghent, in present-day Belgium. The contents of this manuscript suggest that this book was used as an educational treatise for children. Most texts have a didactic nature, such as a text entitled “eenen gheestelicken A.B.C.” [a spiritual A.B.C.], while others focus on the ways in which children should treat their parents, bearing running headers such as “in quade kinderen sal niement verblijden” [evil children will not make anyone happy] and “vader ende moeder moet men in alder noot bijstaen” [one must help one’s father and mother in every need].

The text ‘hoemen boucken bewaren sal om eewelic te duerene’ immediately follows the first ownership inscription and is the first stand-alone text of the manuscript. The prominent place of this text within the manuscript may attest to the educational import of conveying rules of book preservation to a child of the first half of the sixteenth century.

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The Hague, KB 133 F 2, ff. 1v-2r. © The Hague, Royal Library

 

So what does the text actually tell us to do? In the introduction, the author remarks that, if the reader followed his guidelines, books would last “menich jaer[…], ja te minsten twee hondert jaer” [many years…, yes, at least two hundred years]. In short, his eight rules run as follows:

  1. Store your books in a dry and dustless place.
  2. Do not handle your books with dirty fingers.
  3. Do not let your books lie near the fire or leave them open for too long.
  4. Never pull the pastedowns off the boards.
  5. Preserve books from mold and decay, by, for example, not drying it in the winter or touching it with wet fingers.
  6. Do not tear out a page or quire.
  7. Do not doodle or add texts in the margins.
  8. Do not give your books to children.

For each of these rules, the author outlines what would happen if the reader did not follow the rule. For the third rule, for example, the author notes: “want aldus soude den rugghe metten banden crempen ende naermaels ter stont breken” [because this would make the spine shrink with the cords and would make it break immediately].

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Like their users, manuscripts can suffer from back problems. In this case: a broken spine.

 

Do not give your books to children!

Interestingly, the eighth rule (in violation of the seventh rule) was added in the margin only after the text was finished: “Ten 8sten, men sal huut gheenen boucken diemen ter heeren hauwen wilt, de kinderen laten leeren. Want wat in haerlieder handen comt, soe wij sien het blijfter oft het bedeerft.” [Eighth, one should not let children learn from any books that one wants to preserve. Because whatever comes into their hands, as we see, it either stays there or it is ruined]. The rule was added by the same scribe who wrote down the first seven rules. Given that this manuscript was probably used as an educational treatise for children, the addition of the eighth rule may have been due to ‘progressive insight’ on account of the author.

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The Hague, KB 133 F 2, ff. 4v-5r: Eighth rule, written in the margin. © The Hague, Royal Library

Nevertheless, the fact that, with the exception of  the original binding, the book that contains these eight rules is still available in the Royal Library in The Hague in the twenty-first century, proves that the manuscript has far exceeded its expected 200-year life span. We can only conclude, then, that the contemporary and later users of this manuscript abided by the rules outlined above and that they took to heart the moral which was added at the end of the text:

“Men pleegt te segghene an de plume sietmen wat vueghel dat es ende an eens cleercs boucken sietmen wel wat cleerc dat es. Ende alsoe weetmen gheware an de boucken van de lieden of se reijn van ijet te beseghen, goddelic ofte duechdelic van  levene sijn.”

[They say that one can recognise a bird by its plumage, and one can recognise a clerk by his books. And so it will be revealed by the books of people, whether they are clean, god-fearing or good of living.]

medievalkiddoodles

One of the risks of giving books to children: doodles! Here are some examples discovered by book historian Erik Kwakkel (source)

 For those interested in the text ‘Hoemen alle boucken bewaren sal om eewelic te duerene’, an edition and introduction have been published (in Dutch) as: T. Porck & H.J. Porck,‘Hoemen alle boucken bewaren sal om eewelic te duerene. Acht regels uit 1527 over het conserveren van boeken’in: Jaarboek voor Nederlandse Boekgeschiedenis 15 (2008), 7-21. A thoroughly revised, English version of the article, featuring an English translation of the text, is published as: T. Porck & H.J. Porck, ‘Eight Guidelines on Book Preservation from 1527: How One Should Preserve All Books to Last Eternally’, in: Journal of PaperConservation 13(2) (2012), 17-25. The English article is available on Academia.edu.

Works referred to:

  • Clark, John (1902). The Care of Books. Cambridge: Cambridge University Press.
  • De Bury, Richard. Philobiblon. Ed. and trans. by E.C. Thomas (1888).
  • Lem, Constant, (1991). ‘De Consuetudines van het Collatiehuis in Gouda.’ Ons Geestelijk Erf 65, 125-143.

This is an edited version of a blog previously posted on the medievalfragments blog.

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Flashed after the Flood: Seeing naked fathers in Anglo-Saxon England

In honour of Father’s Day (19-06-2016), this blog post calls attention to three Anglo-Saxon responses to the story of Ham seeing his father Noah’s nakedness (Genesis 9:21-25). This intriguing biblical tale inspired one Anglo-Saxon artist to draw what may be one of the most x-rated illuminations of the early Middle Ages.

Seeing his father’s nakedness in The Illustrated Old English Hexateuch

The Illustrated Old English Hexateuch (The British Library, Cotton Claudius B.iv) contains an Old English translation of the first six books of the Bible and is lavishly illustrated with over 400 illuminations (you can find out more about this fascinating manuscript here: The Illustrated Old English Hexateuch: An early medieval picture book). Since the Old English translation (written in part by Ælfric of Eynsham) follows the Latin Vulgate closely, the Illustrated Old English Hexateuch is a good place to start exploring how the story of Ham witnessing his father’s nakedness circulated in Anglo-Saxon England.

We find the story in Genesis 9:21-25. After relating how Noah survived the Flood in his ark, the biblical account continues with Noah’s building of a vineyard and tasting the fruits of his efforts:

7 ða ða he dranc of ðam wine, ða wearð he druncen 7 læg on his getelde unbehelod. His sunu ða, Cham, geseah his gesceapu unbeheled, 7 cydde hit his twam gebroðrum ut on felda.

[And  when he drank of the wine, then he became drunk and he lay naked in his tent. Ham, his son, then saw his naked genitals and made it known to this two brothers out in the field.]

The artist of the Old English Hexateuch captured these three actions in the following marvellous illustration (note how Ham sneaks around the frame to peek at Noah in his multi-coloured tent) :

FathersNakedness1

Noah getting drunk with wine (top left); Ham seeing his father’s nakedness (right) and Ham telling his brother Sem and Japhet (bottom left) © The British Library, Cotton Claudius B. IV, fol. 17v

The biblical account continues with Sem and Japhet showing more restraint than their voyeurish brother:

Hwæt, ða Sem 7 Iapheth dydon anne hwitel on heora sculdrum, 7 eodon underbæc 7 beheledon heora fæderes gecynd, swa ðæt hi ne gesawon his næcednysse.

[Lo! Then Sem and Japhet took a mantle over their shoulder and went backwards and covered their father’s genitals, so that they did not see his nakedness.]

The artist once again captures this biblical verse perfectly (one of the brothers is slightly overdoing it: not only walking backwards but shielding his eyes with his cloak at the same time!):

FathersNakedness2

Sem and Japhet covering up Noah © The British Library, Cotton Claudius B. IV, fol. 17v

Noah then awakes from his sleep:

Noe soðlice ða ða he awoc of ðam slæpe, 7 he ofaxode hwæt his suna him dydon. Ða cwæð he: Awyrged is Chanaan, 7 he byð ðeowena ðeowa his gebroðrum.

[Truly, Noah, when he awoke from sleep,  asked what his sons had done to him. Then he said: ‘Cursed is Canaan [Ham’s son] and he will be the slave of slaves for his brothers.’]

The artist now shows an awake Noah (still in a floating cocoon!) addressing Sem and Japhet (who are about to blessed).This time, Ham, whose offspring has just been cursed, has his face turned from his father (too little, too late!):

FathersNakedness2b

Noah cursing Ham’s son Canaan  © The British Library, Cotton Claudius B. IV, fol. 18r

The Venerable Bede and the various  explanations of Ham’s punishment

As you can tell, the biblical account is rather brief and leaves much to the imagination, especially since cursing the son of your son to a life of servitude seems a rather harsh punishment for an act of voyeurism. Due to the obscurity of many of the details of the story, interpretations of Ham’s seeing Noah’s nakedness have run wild. The phrase “seeing your father’s nakedness”, in particular, has led some interpretators to refer to Leviticus 18:6-19, where the phrase “uncovering someone’s nakedness” implies sexual activity: Ham may have masturbated his drunk father or, perhaps worse, sent in his youngest son Canaan to perform this act (since it is Canaan that is cursed!) (see: UK Apologetics). Others have suggested that Ham did not have any sexual dealings with Noah himself, but with Noah’s wife (cf. Leviticus 18:8: “Thou shalt not uncover the nakedness of thy father’s wife: for it is the nakedness of thy father”; see: New World Encyclopedia ). Did Ham sleep with his own mother while his father was drunk ? Scandalous!

The Anglo-Saxon monk and scholar Bede (d. 735) did not imagine anything other than Ham simply seeing the nakedness of his father. What made Ham’s actions so repulsive, Bede wrote in his commentary On Genesis, was not just the act of seeing, but the act of making it public knowledge. What’s more, Bede added that Ham had laughed at his father’s nakedness and he linked Ham’s actions to how the Jews had derided Christ:

Ham, who laughed when he saw that his father’s private parts were uncovered, signifies the insulting and incredulous Jewish people, who rejoiced rather to hold in contempt the passion of our Lord and Saviour to their own destruction than, for the sake of being saved, to be glorified by it. (trans.  Kendall, p. 210)

Bede also weighed in on why Ham’s son Canaan was punished, rather than his father:

And according to the literal sense it should be noted also that, although Ham sinned, there is a reason why not he but his son Canaan is cursed, especially since the latter was not the first-born of Ham, but his last son. … For at the same time it was foreseen on the spiritual level that the offspring of Canaan were going to sin much more than the other offspring of the sons of Ham, and therefore that they would deserve either to perish by the curse or to groan under the slavery to which they were subjected. (trans. Kendall, p. 213)

Bede goes on to explain that the inhabitants of Sodom and Gomorrah (Genesis 19:24-30) descended from Canaan. Thus, since God had foreseen the transgressions of the Canaanites, the curse on Canaan and his descendants was anticipatory punishment! (for the story of Sodom and Gomorrah and its depiction in the Old English Hexateuch click here)

Laughing at his father’s genitals in the Old English Genesis

Bede was not the first to add to the biblical narrative the idea of Ham laughing at his father’s exposed state; the idea goes back as far at least as the theologian Origen (c. 185-c. 254; quoted here). Nor was Bede the last. The poet responsible for the Old English verse adaptation of Genesis (full text available here) made the same addition to the story:

ða þæt geeode,      þæt se eadega wer
on his wicum wearð      wine druncen,
swæf symbelwerig,      and him selfa sceaf
reaf of lice.      Swa gerysne ne wæs,
læg þa limnacod. …

þa com ærest      Cam in siðian,
eafora Noes,      þær his aldor læg,
ferhðe forstolen.      þær he freondlice
on his agenum fæder      are ne wolde
gesceawian,      ne þa sceonde huru
hleomagum helan,      ac he hlihende
broðrum sægde,      hu se beorn hine
reste on recede. (Genesis, ll. 1562-6, 1577-85)

[And then it happened that the blessed man became drunk of wine in his dwellings, he slept weary of feasts, and he himself cast the cloth from his body. Then he lay naked of limb, as it was not fitting.  …  Then Ham, the son of Noah, first went in, where his elder lay, deprived of mind. There he did not want to look upon his father with reverence, nor conceal his shame from their kinsmen. But, laughing, he told his brothers how the man rested in his dwelling.]

Interestingly, the Anglo-Saxon poet has Noah then curse Ham, rather than his youngest son Canaan – thus avoiding any confusion.

This Old English poetic version of Genesis is found in the early-eleventh-century manuscript Oxford Bodleian Library, Junius 11. Like the Old English Hexateuch, this manuscript is beautifully illustrated and the artist responsible also captured the various scenes that make up the story of Ham uncovering his father’s nakedness:

FathersNakedness3

Ham seeing his father’s nakedness (top); Ham telling his brothers (middle); his brothers covering Noah (bottom). (c) Oxford, Bodleian Library, Junius 11, p. 78 (source)

One of the striking features of this illustration is the explicit depiction of Noah’s genitals. Whereas the artist of the Illustrated Old English Hexateuch obscured our view by having Noah conveniently raising up his legs, the artist of Junius 11 gives us the whole stick and balls:

FathersNakedness4

Top: Noah lifting up the covers to expose his genitals in Oxford, Bodleian Library, MS Junius 11, p. 78 (source); bottom: Noah’s genitals obscured by his legs in The British Library, Cotton Claudius B.IV, fol. 17v.

Perhaps, the artist of Junius 11 wanted to test his audience with this particular illustration: he gives us the choice to look upon Noah’s genitals (like Ham) or avert our eyes (like Sem and Japhet). If so, I failed the test!

Works referred to:

  • Bede, On Genesis, trans. C. B. Kendall (Liverpool, 2008)

The Battle of Maldon: A Student Doodle Edition

For a bonus question on one of my Old English literature exams, my students used their artistic talents to draw scenes from The Battle of Maldon. Together, these doodles cover almost the entire poem and document how well (or how badly) my students remembered the poem.

Drawings have long since been used for the purpose of teaching (for an example from the Anglo-Saxon period see Teaching the Passion to the Anglo-Saxons: An early medieval comic strip in the St Augustine Gospels). On occasion, I use my own drawings to spice up my lectures (such as my Anglo-Saxon Anecdotes) or explain complicated bits of Anglo-Saxon literature (e.g., The Freoðuwebbe and the Freswael: A Comic Strip Reconstruction of the Finnsburg Fragment and Episode). For last year’s third-year Old English literature exam, I decided to turn the tables on my students. I had them each draw a scene from the Old English poem The Battle of Maldon for a bonus point (worth 1% of the final grade) and the results were both hilarious and insightful. While the exercise was intended as a bit of a gag, their doodles actually allowed me to see which events from the poem had captured their interest; how they (mis)remembered certain passages; how few of them could spell the name of the English leader Byrhtnoth correctly; and which scenes, apparently, made no impact on them at all (e.g., no one pictured the loyal retainers fighting on to die alongside their lord!).  Here follows a selection of my students’ drawings, along with some commentary.

i) Release the hawk!

BomDoodle1

In the opening lines of the extant version of The Battle of Maldon, the kinsman of Offa releases his “leofne…hafoc” [beloved hawk] (ll. 4-5); a scene, which apparently, struck a chord with these two students. As the second student points out, Offa’s release of the hawk, as well as the decision of the English to drive away their horses, was  intended to strengthen the morale of the English troops – they had burned their bridges (or: released their beloved hawks) and there would be no turning back!

ii) ‘Give us dollah!’

BomDoodle2.jpg

The next two students have drawn how the Vikings demand tribute or, as the second drawing suggests, “dollah”, which (apparently) is slang for money or danegeld [the term used for the tribute paid by the Anglo-Saxons to the Dane – bonus point!]. The English respond reluctant: “not a chance!” according to the first student; the second student is closer to the mark: “kill them with spears!”, “poisoned spears!”, some of the English shout – reflecting the English leader Byrhtnoth’s original response to offer the vikings “garas …ættrynne ord and ealde swurd” [spears, poisoned spears and old swords] (ll. 46-47) .The second drawing also shows what happens next: the Vikings ask to be allowed to pass and “Byrthroth” lets them – an important scene that inspired many other students as well…

iii) Let them pass!

BomDoodle3

This student has drawn the strategic advantage of the English army, led by “Byrhnoth”: the Vikings had to cross a narrow tidal causeway to get to the other side. (Ooo! Horned helmet alert!)

BomDoodle4.jpg

This student has the Vikings threaten to “hurt you and your mum”; stick figure “Byrhnoth” is unimpressed and says “You may cross over so we can fight like real men. I want glory!”.

BomDoodle6

This student depicts “Brythnots army standing by while Vikings get on British lands”. With a keen eye for detail, the student has the English play games of football, chess and whiff-whaff (and one English warrior even sleeps in a hammock!), while the Vikings cross to the main land.

BomDoodle7

Another bridge-crossing scene – one English warrior shouts “Yay! Fair battle!” and another shouts “Swilce ofermod!”. The latter, of course, refers to the original poet’s remark that the English leader Byrhtnoth acted out “his ofermode” (l. 89) [his excessive pride].

iv) The beasts of battle await…

BomDoodle12This student has remembered one of the recurring typescenes of Old English heroic poetry: the beasts of battle that show up at the end of a battle to devour the dead bodies. They also make an appearance in The Battle of Maldon: hremmas wundon / earn æses georn” [ravens wound about, eager eagles of carrion] (ll. 106-107).

v) The death of Byrhtnoth

BomDoodle8

I always tell my students that this scene is pure Hollywood: the old leader “Byrnthoth”  – a “har hilderinc” [grey-haired warrior] (l. 168) – goes down, the young warrior Wulfmær – “hyse unweaxen” [a young man, not fully grown] (l. 152) –  takes revenge! I am glad that at least one of them took note. Not sure where the broken sword comes from though…

BomDoodle9

Another student also remembered the scene (and the correct spelling of the leader’s name!), and then went all Harold Godwinson on the offending Viking spear-thrower!

vi) How not to be a hero

BomDoodle10

Of course, not all English warriors were as courageous as young Wulfmaer. This student remembers how the sons of Odda fleed the scene, taking with them the horse of their stricken leader “Byrtnoth”. In the poem, all three sons of Odda flee the scene and, in the mind of the next student, they all did so on the same horse:

BomDoodle11

I find it intriguing to see how none of the students seem to have been inspired to draw the near-suicidal loyalty of the English warriors after their lord has been cut down. Even the poem’s most famous lines “Hige sceal þe heardra, heorte þe cenre / mod sceal þe mare, þe ure mægen lytlað” [Mind must be tougher, heart must be bolder, courage must be greater, as our strength becomes less]  did not get a mention – odd, given that it is the perfect mindset for an exam!

vii) Wow, very ofermod, much Anglo-Saxon, wow

BomDoodle13.jpg

Wow, indeed.

Alcuinundrums: Seven brain teasers from the early Middle Ages

A wolf, a goat and a cabbage. You have one boat and need to get all three across safely. Many will be familiar with this river crossing puzzle or one of its variants. The earliest known instance of this puzzle dates back to the early Middle Ages and is found in a peculiar work attributed to Anglo-Saxon monk and scholar Alcuin of York. This blog post calls attention to Alcuin’s mathematical puzzles and invites you to a game of medieval brain training!

Alcuin of York (c. 735-804) and the Propositiones ad acuendos iuvenes

Possibly the most knowledgeable scholar of his age, the Anglo-Saxon Alcuin of York (c.735–804) made a career at the Carolingian court of Charlemagne (d. 814). He was an advisor to Charlemagne himself and taught the royal children at the Palace School. This Northumbrian monk quickly became recognised as one of the court’s foremost scholars and he wrote many poems, letters and books on various topics, including grammar, orthography, theology and hagiography.

Deep in his heart, Alcuin always remained a teacher, as he made clear in a letter to Charlemagne:

I shall not be slow to sow the seeds of wisdom among your servants in these parts, as far as my poor talent allows. … In the morning, at the height of my powers, I sowed the seed in Britain, now in the evening, when my blood is growing cold, I still am sowing in France, hoping both will grow, by the grace of God. (trans. Allott 1974, let. 8)

As a result, many of his works were of a didactic nature and perhaps the most peculiar of these bears the title Propositiones ad acuendos iuvenes [Propositions to Sharpen the Young]. This text is a collection fifty-three mathematical puzzles, which were intended to make mathematics palatable for students (a noble cause!). The collection includes, as noted above, the earliest attestation of the famous wolf-goat-cabbage-river cross problem (which is so famous that the Internet features several games that allow you to solve this problem, such as this one featuring ‘Sailor Cat’). Aside from various river crossing problems, the collection includes puzzles that involve mathematical and geometric calculations. To make the puzles relatable for his students, Alcuin wrote them in the form of little stories, involving men sharing oxen, pigeons sitting on staircases, families crossing rivers and dogs chasing hares (Yes, teaching mathematics through story has a long history, indeed!). Alcuin even included some trick questions, such as “An ox ploughs a field all day. How many footprints does he leave in the last furrow?”. The answer to that last question, of course, is ‘none’, since the ox precedes the plough and, therefore, all of its footprints are erased!

Below follow seven of Alcuin’s brain teasers. Some may test your wits, while others may require a piece of paper. If you want the real medieval experience, do not use a calculator! The solutions are provided at the end of this blog post. The translation of the Propositiones ad acuendos iuvenes is that of John Hadley (Hadley & Singmaster 1992):

i) Don’t sink the boat!

Alcuinundrums.Boat

Woman, man, two children and a boat, c. 1400 © The British Library, Royal 10 E IV, f. 122v

A man and woman, each the weight of a cartload, with two children who together weigh as much as a cartload, have to cross a river. They find a boat which can only take one cartload. Make the transfer if you can, without sinking the boat.

ii) A dog chasing a hare

Alcuinundrums.doghare

Dog chasing a hare in thirteenth-century manuscript © The British Library, Harley 928, f. 10

There is a field 150 feet long. At one end is a dog, and at the other a hare. The dog chases when the hare runs. The dog leaps 9 feet at a time, while the hare travels 7 feet. How many feet will be travelled by the pursuing dog and the fleeing hare before the hare is seized ? [i.e., how long will it take the dog to overtake the hare which has a 150 feet head start?]

iii) Buying camels, sheep and asses

Alcuinundrums.camels

Camels in the Old English Hexateuch © The British Library, Cotton Claudius B.iv, f. 48v

A man in the east wanted to buy 100 assorted animals for 100 shillings. He ordered his servant to pay 5 shillings for a camel, one shilling for an ass and one shilling for 20 sheep. How many camels, asses, and sheep did he buy ?

iv) A stair case of pigeons

Alcuinundrums.pigeons

Pigeons in fourteenth-century manuscript © The British Library, Royal 2 B VII, f. 117v

A staircase has 100 steps. On the first step stands a pigeon; on the second two; on the third three; on the fourth 4; on the fifth 5. And so on, on every step to the hundredth. How many pigeons are there altogether?

v) A flock of storks

Alcuinundrums.Stork

Stork in fifteenth-century manuscript © The British Library, Additional 16577, f. 41v

Two walkers saw some storks and wondered how many there were. Conferring, they decided: if there were the same number again, and again, and then half of a third of the sum that would make, plus two more, that would be 100. How many storks were seen ?

vi) Evening out the oxen

Alcuinundrums.oxen

Oxen in fourteenth-century manuscripts © The British Library, Royal 2 B VII, f. 75

Two men were leading oxen along a road, and one said to the other: “Give me two oxen and I’ll have as many as you have”. Then the other said: “Now you give me two oxen and I’ll have double the number you have.” How many oxen were there, and how many did each have?

vii) Slaughtering pigs

Blog.Alcuinundrums

Dutch Anglo-Saxonist and an even number of Anglo-Saxon pigs at Bede’s World, Jarrow

A certain man had 300 pigs. He ordered all of them slaughtered in three days, but with an uneven number being killed each day. He wished the same thing to be done with 30 pigs. Let him say, he who can, What odd number of pigs out of 300 or 30 were to be killed in three days?

Solutions

Raban-Maur_Alcuin_Otgar

Alcuin (middle) with Raban Maur (left) and Archbishop Otgar of Mainz (right) (SOURCE)

  • i) The kids do most of the rowing! First: the two kids go to the other side, one rows back. Next, one of the parents rows to the other side. Then, the kid who had stayed on the other side goes back alone and picks up the other child and goes to the other side again. Now, the two children and one of the parents are on the other side, while one parent has stayed behind. One child rows to the missing parent, the missing parent rows to the other side – the child who is now with two parents rows back to pick up his sibling and -hurray- the family is reunited again!
  • ii) The hare has a head start of 150 feet, but the dog goes 2 feet per leap faster. In other words, it will take the dog 150/2=75 leaps to catch up to the hare. The dog will have travelled 75*9 = 675 feet, while the hare would have travelled 75*7 = 525 feet.
  • iii) For 5 shillings you have 100 sheep and 95 shillings to spare! But that would be cheating, of course. The trick is to buy 80 sheep for 4 shillings, 1 ass for 1 shilling and then spend the other 95 shillings on 19 camels.
  • iv) The answer is 5050. Alcuin outlines an easy way of calculating this total:

    We count them as follows. Take the single one on the first step and add it to the 99 on the ninety-ninth step, making 100. Taking the second with the ninety-eighth likewise gives 100. So for each step, one of the higher steps combined with one of the lower steps, in this manner, will always give 100 for the two steps. However the fiftieth step is alone, not having a pair. Similarly the hundredth remains alone. Join all together and get 5050 pigeons.

  • v) 100-2 = 98. 98 is three and a half times the original number; 98 divided by 3.5 = 28. So they originally saw 28 storks!
  • vi) There were 12 oxen. The first man had 4 oxen and the other 8 – if the first man received 2 oxen from the other, they would both have 6. If the other would get his 2 oxen back, we would be back to the initial situation: 4 against 8.
  • vii) Aha! Alcuin is trying to trick us here. His own solution runs as follows “This is a fable. No-one can solve how to kill 300 or 30 pigs in three days, an odd number each day.” He then notes that this trick question is to be given to (misbehaving) children. That would teach them! (I am not sure whether Alcuin’s reasoning is didactically sound here!)

Works referred to:

  • S. Allott (trans.), Alcuin of York: His Life and Letters (York, 1974)
  • John Hadley (trans.) & David Singmaster, ‘Problems to Sharpen the Young’, The Mathematical Gazette 76 (1992), pp. 102–126.

Post Scriptum: As @AlcuinsLibrary  has rightly pointed out to me, most of the puzzles in the Propositiones stem from a long tradition and were certainly not made up by Alcuin (although some occur here for the first time). In fact, Alcuin’s authorship itself is a matter of conjecture rather than fact (some manuscripts attribute the puzzles to Bede). Alcuin’s authorship is suggested (but not proven) by a letter that he wrote to Charlemagne in which he talks of having sent “certain subtle figures of arithmetic, for pleasure” (Hadley & Singmaster 1992). These pleasurable figures of arithmetic may or may not have been the Propositiones