Solution
We plan to put Beauty to sleep by means of a pill, and then we'll flip a fair coin. If the coin lands heads, we will awaken Beauty on Monday afternoon and interview her. If it lands tails, we will awaken her Monday afternoon, interview her, put her back to sleep, and then awaken her again on Tuesday afternoon and interview her again.
Each interview is to consist of the one question: what is your credence now for the proposition that our coin landed heads?
When awakened (and during the interview) Beauty will not be able to tell which day it is, nor will she remember whether she has been awakened before.
She is told the above details of our experiment beforehand.
What probability should she give to the coin landing heads?