A man has a single coin in front of him that lands on heads with probability p and tails with probability 1-p. He begins flipping coins with his single coin. If a coin lands on heads it is removed from the game and n new coins are placed on his stack of coins, if it lands on tails it is removed from the game and no new coins are introduced. What is the condition on n and p for the man to have a non-zero probability of playing forever? For an easier challenge check out Challenge 12a. This is a harder challenge than it may appear at first glance; points may be awarded for a mildly non-rigorous solution (and bonus points for a fully rigorous solution).