Aside from well known examples of mathematics contests in 1535 and 1548, what are some other examples before 1800?
Background: In The History of Mathematics: an Introduction, 3rd edition (1995), David Burton mentions the contests between Nicolo Tartaglia and Antonio Maria Fiore in 1535 (p. 292) and between Tartaglia and Ludovico Ferrari at Milan in 1548 (p. 302). Burton writes (p. 290): “It was the practice in those days to treat mathematical discoveries as personal properties, disclosing neither method nor proof, to prevent their application by others to similar problems. This was because scholarly reputation was largely based on public contests. Not only could an immediate monetary prize be gained by proposing problems beyond the reach of one’s rival, but the outcomes of these challenges strongly influenced academic appointments; at that time, university positions were temporary and subject to renewal based on demonstrated achievement.”
Does there exist a fuller description of these "public contests"? Is there a published list of examples? I would especially like to see statements of the problems, along with names, dates, etc.