I'm not going to explain the sleeping beauty paradox here. If you don't know it, I recommend you read up on it.
Here is another version of the paradox, that is a bit more complicated: In the case of heads, sleeping beauty is awakened the next day, as in the normal version and the experiment ends after that. But in the case of tails, they are awakened the next day, questioned, and then the experiment is reset to the start. A new coin is tossed and if it's heads, they go through one more round of questioning and are done, whereas tails means that they just start again. This continues for as long as it takes until a heads comes up. Every time the experiment is repeated, a counter is increased that keeps track of the amount of iterations, but this counter is inaccessible to both sleeping beauty and the experimenter. The experiment is carried out in parallel, and a new version of the experiment is started every time sleeping beauty is questioned. The answer sleeping beauty gives to the question is recorded in a sealed envelope, which is added to the stack of envelopes for all other instances of sleeping beauties on that given day. The stack is shuffled and an envelope is drawn at random. If the same sleeping beauty is selected this way on two consecutive days, the universe is split into two different versions, that are completely identical but future coin tosses are still independent (so their past is identical but their future may diverge, i.e., determinism does not hold).
Oh, right, because there are multiple coin tosses involved, the question we pose to the sleeping beauty must be slightly altered. Instead of asking for the result of a coin toss, they are asked what their credence is that the sleep and amnesia inducing drug has unintended side effects.
