Confucius said, “When you are in the presence of a leader, you risk making three mistakes. To speak about something before the appropriate time is to be impetuous; to fail to speak about something at the appropriate time is to be evasive; to speak without observing the expression on their face is to be blind.”
I have no idea why the editors of Book 16 of the Analects decided that three is a magic number. Be warned: there are more such lists to come.
It’s never easy to know when to talk and when to shut up when you are meeting someone for the first time, particularly if they are more “important” than you. Probably the most practical advice this passage contains is to watch the person you are talking to as closely (and discretely) as possible in order to determine whether they are bored or interested by what you have to say.