The 'Sleeping Beauty problem' is a philosophical / mathematical logic 'thought experiment' first devised (in a slightly different form) in 1990.

It currently has two different answers, one of which, presumably, must be wrong.

The Sleeping Beauty problem: Some researchers are going to put you to sleep. During the two days that your sleep will last, they will briefly wake you up either once or twice, depending on the toss of a fair coin (Heads: once; Tails: twice). After each waking, they will put you to back to sleep with a drug that makes you forget that waking. When you are first awakened, to what degree ought you believe that the outcome of the coin toss is Heads?

Source : Analysis, 60(2): 143-147, 2000. Adam Elga, MIT

It's considered that there are two possible answers : either ½ or ⅓ .

There are convincing mathematical arguments for both results - but only one can be correct. So far, more than 100 academic papers have been published on the subject (refs. ) But the mathematical and philosophical communities cannot currently agree on which is the right answer.

( Note that the origin of the problem came from a paper by Arnold Zuboff (Princeton / UCL) in Inquiry: An Interdisciplinary Journal of Philosophy 33 (1):39-68 (1990) entitled : One self: The logic of experience , and later re-presented as a PhD dissertation in 2009 )