# Four Medieval Manuscripts With Mathematical Games

Four Medieval Manuscripts With Mathematical Games

Eldredge, L.M.; Schmidt, Kari Anne Rand; Smith, M.B.

Medium Aevum, Vol. 68 Issue 2, (1999)

Introduction: In the course of our research for the Index of Middle English Prose, we have come across some interesting variants of two types of mathematical game, both representative of a genre of some antiquity and apparently wide distribution. Both types of game are designed to impress and mystify, and they are also of particular interest for the evidence they provide of considerable exploration into numerical relationships. In fact it is clear from the work of others that these are not the only manuscript instances of such amusements, and perhaps this article will help to reveal the whereabouts of ones previously unrecognized. Two of these games are versions of a puzzle that has come to be known as the Josephus Problem. It seems to date from an incident recounted in Josephus’ De bello Judaico, which involves the author himself. At the siege of Jotapata, Josephus finds himself in a position of either surrendering to Vespasian’s troops or participating in a mass suicide with some forty Jewish soldiers. Outvoted, Josephus arranges the soldiers in such an order that every nth soldier is to be killed, the final survivor to commit suicide. Without explaining his precise procedure, Josephus relates that he is the survivor and is thus able to surrender and save his skin.

One late version of the Josephus Problem is found in Oxford, Bodleian Library, MS Bodley 496, a fifteenth-century paper manuscript, written in England and containing mostly medieval Latin poetry. On fol. [215.sup.v], immediately following a Latin poem of some ninety lines dealing with a dissolute and drunken village priest (fols [214.sup.v] – 215), there is a versified version of the problem which involves fifteen Christians and fifteen Jews at sea in a boat that threatens to capsize in a storm. In order for any lives to be saved, half of those on the vessel must be thrown overboard; so it is decided that the passengers will be counted off and every tenth person sacrificed. The problem is to arrange those on board so that in the process all the Christians will survive. In other versions of this problem, discussed below, there is a mnemonic line the arrangement of whose vowels indicate to the adept the correct placement of the persons. In Bodley 496 there are mnemonic verses that explicitly state what the arrangement should be. The text of the verses follows, with abbreviations silently expanded, punctuation added, and emendations in pointed brackets.