Some folks say it reminds them of "The Monty Hall Problem" in so much as people argue vigorously for different solutions. But the Monty Hall Problem has an actual correct answer, whereas (so far as I can tell) the SBP really can be argued in two different, divergent approaches (designated as "halfers" and "thirders"). The paradox is sometimes stated in slightly variable ways, which is part of the problem, but even a fairly standard statement of it can include slight semantic pitfalls, leading to some of the disagreement. Still, more than 'Monty Hall,' the SB problem reminds me of the famous "Newcomb's Paradox" where people also tend to split two ways, and there simply is no established "right" answer.
Wikipedia states the SB problem as follows:
"Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details. On Sunday she is put to sleep. A fair coin is then tossed to determine which experimental procedure is undertaken. If the coin comes up heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday and Tuesday. But when she is put to sleep again on Monday, she is given a dose of an amnesia-inducing drug that ensures she cannot remember her previous awakening. In this case, the experiment ends after she is interviewed on Tuesday.
Any time Sleeping beauty is awakened and interviewed, she is asked, "What is your credence now for the proposition that the coin landed heads?"
Many re-state the problem to ask Sleeping Beauty, "What is the probability now for the proposition that the coin landed heads?," and some argue this word change is significant and alters the discussion. I think most people however, indeed understand the problem in terms of probabilities (the probability of heads being either 1/3 or 1/2), and so I certainly prefer thinking about it that way.
The Wikipedia entry for the problem is here:
And here are some more links discussing it (warning though, they may cause your head to pound ;-)):
http://blog.tanyakhovanova.com/?p=356 (arguing for the 1/3 answer)
http://barryispuzzled.com/zbeauty.htm (arguing for the 1/2 answer)
…and discussion from a "freethought forum" here:
Finally, if that's not enough for you, you glutton-for-punishment, more links here: