# Sleeping Beauty

The Grey Labyrinth recently received the following memo from the Newcomb Institute of Technology:

"In the 1999, the Newcomb Institute of Technology diversified their studies from the original Newcomb Problem to a wider range of epistemic paradoxes, including the performing of the following experiment:

A volunteer was recruited from the philosophy department of a nearby University.

The subject, whom we will refer to as "S.B." was privy to all the details of the experiment in advance, and participated willingly.

One Sunday evening, S.B. went to sleep at the NIT observation labs. In another part of the labs a fair coin-toss was conducted, yielding a result of heads or tails. S.B. Was aware that the coin-toss was made, but not the results of the toss. However, she was made aware that the following events would transpire, dependent on the results of the toss:

If the toss came up heads, S.B. would be awoken at 6AM on Monday morning and asked what the probability was that the coin had come up heads.

If the toss came up tails, S.B. Would be awoken at 6AM on Monday morning and asked what the probability was that the coin had come up heads. BUT, on Monday evening she would be given an amnestic, putting her to sleep and totally clearing her memory of the previous 24 hours. Then, on Tuesday morning she would be awoken at 6AM and asked what the probability was that the coin had come up heads.

The amnestic had no side effects other than removing the previous days memories and resetting her body's internal clock back 24 hours. Upon awaking, S.B. had no certain way of knowing whether the amnestic had been administered, or what day it was."

Now as curious puzzlers, we can't help but wonder what we would do in S.B.'s place. Would we answer 1 in 2, or 1 in 3?

(This clever paradox is based on one that appeared in the rec.puzzles newsgroup. I believe it to be by an MIT graduate student named Adam Elga.)