Thomas Bradwardine and Richard Kilvington were two young philosophers at Oxford in the 1320s. Much of their training as students and young masters of philosophy was to engage in disputations. Some of those disputations are "obligational disputations", in which the respondent was obliged to try to maintain a position consistently in response to challenges from the opponent. The language of these disputations runs right through their writings on sophisms (puzzles of various sorts) and insolubles (even trickier puzzles). One of the hardest puzzles preserved in Kilvington's treatise on Sophisms raised problems which Bradwardine seems to have tried to solve using the techniques in his treatise on Insolubles. In this lecture, I'll try to explain, for those new to the world of medieval logic, the rigours of the obligational method, the nature of Kilvington's puzzle and the idea behind Bradwardine's solution.