David, thanks very much for your concise answer which is absolutely correct. Moreover, I’m delighted to have you comment on this blog for a number of intersecting reasons. Firstly, because I think your work is very interesting. Secondly and serendipitously, I note from your webpage that you attended the “Mathematics and Narrative” conference on Mykonos, which has been reported in Nature and which I have been enthusing my colleagues about. Thirdly, and perhaps most trivially (or perhaps not) we both work at a “University of Canterbury”, albeit antipodally (and with a “Kent at” inserted, in your case)

edgarsr, I suppose that the assumption that the choirmaster and the vicar would know each other’s ages is a “hidden fact”. Vicars and choirmasters usually work quite closely and so would know each other reasonably well. But perhaps the church-based setting of this puzzle is too old-fashioned now.

Does anybody have any suggestions for updating this puzzle to a modern setting?

The only two triples with this property are (49, 10, 5) and (50, 7, 7). (So he’s 32.)

Now we’re told that the choirmaster can distinguish between these triples on hearing a piece of information which bounds the upper age. It can only be because the choirmaster knows that the age of the vicar is 50. Any older and neither triple would be ruled out.

Thanks for your answer, David. Would you like to share how you got it, then we can see if it is correct?

Edgar, no hidden facts are required (at least, no hidden facts about vicars). You might want to look at your list again. Are there other alternatives? For example, 7, 7, 50 . . .

So, it is only known vicar ir older than 49. Am I missing something??