When is Lonnie train ?

Lonnie is taking the train to the Library. He tells Rosti the hour of his train’s departure and he tells Ann at which minute it leaves. He also tells them both that the train leaves between 0600 and 1000.

They consult the timetable and find the following services between those two time:
0632 0643 0650 0717 0746 0819 0832 0917 0919 0950

Rosti then says “I don’t know when Lonnie’s train leaves but i am sure that neither does Ann”

Ann Replies “I didn’t know his train, but now i do”

Rosti responds “Now I do as well!”

When is Lonnie’s train and how do you know?

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Answer: 0832

Rosti knows the hour but knows that Ann doesn't know, so it must be an hour with no unique minutes.
It can't be 06 because that has 0643 and 43 is unique.
It can't be 07 because 46 is unique.
So the hour must be 08 or 09.

Once Ann has worked this out, if she knows the time it must be at minutes that aren't shared between 08 and 09. So it must be 08:32, 09:17 or 09:50.

Rosti now knows the exact time, so it must be 08:32.