If you announce in advance someone will be speaking, it is no longer impromptu but rather scheduled?
That reminds me of an old but deep puzzle.
Suppose Belichick announces on Sunday that there will be an impromptu press conference after practice some day in the next week: Monday, Tuesday, Wednesday, Thursday or Friday. (Assuming this is a week where there is a practice each weekday).
But he says that nobody (well except him) will know on what day the press conference is scheduled until after practice that day. Nobody can have
foreknowledge of the press conference.
What day is the impromptu press conference?
(*) It cannot be
Friday, because if the press conference had not been held by Friday then everyone would know on Friday morning when the press conference would held. Indeed, on Friday morning, they would know it must be held after practice Friday, the last day.
So everyone must know, on Monday, that the press conference won't be on Friday, but instead only on one of Monday, Tuesday, Wednesday or Thursday.
(**) But likewise the press conference cannot be on
Thursday, since, if it had not been held by Thursday morning, everyone would reason that the conference could not be held Friday (by (*) above), so they would know that morning that the conference must be held on Thursday, contradicting the requirement of lack of foreknowledge.
Hence, by (**) and (*), everyone would know, by Monday, that the conference must be held on Monday, Tuesday, or Wednesday.
But the same reasoning as in (*) and (**) applies here: the conference could not be held on Wednesday, Tuesday, or Monday, using exactly the same reasoning.
The paradox is this: by the above reasoning, everybody knows that Belichick cannot be telling the truth: he cannot hold this impromptu press conference in such a way that nobody but him knows when it will be until after practice.
Belichick holds the conference on Wednesday anyway, and in fact nobody knew it would be held then until after the game, just as he said. So he was telling the truth and everybody was wrong.