You could choose to join the debate on the Sleeping Beauty puzzle...
Here's the short version from the link below...
Usually, there are clear answers in mathematics—especially if the tasks are not too complicated. But when it comes to the Sleeping Beauty problem, which became popular in 2000, there is still no universal consensus. Experts in philosophy and mathematics split into two camps and ceaselessly cite—often quite convincingly—arguments for their respective side. More than 100 technical publications exist on this puzzle, and almost every person who hears about the Sleeping Beauty thought experiment develops their own strong opinion.
The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
www.scientificamerican.com
Here's the short version from the link below...
Usually, there are clear answers in mathematics—especially if the tasks are not too complicated. But when it comes to the Sleeping Beauty problem, which became popular in 2000, there is still no universal consensus. Experts in philosophy and mathematics split into two camps and ceaselessly cite—often quite convincingly—arguments for their respective side. More than 100 technical publications exist on this puzzle, and almost every person who hears about the Sleeping Beauty thought experiment develops their own strong opinion.
The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake
A thought experiment that’s dividing mathematicians can help illuminate how belief shapes rational decisions
