The Sleeping Beauty Problem

Sleeping beauty is put to sleep and a coin is flipped. If the coin lands on heads, she is woken up on Monday. If the coin lands on tails, she is woken up on Monday, put back to sleep, and woken up again on tuesday. Sleeping beauty forgets what happened on Monday when she is put back to sleep. When she is woken up, she is asked the probability that the coin landed on heads. What should she answer? This is a controversial problem in the statistics community where some experts say she should answer 1/2, while others say the answer is 1/3.