MathNet 2012 Question 67

Martino thinks he has discovered a method for winning at roulette, or at least not losing too much money. He always bets on red. He starts with a bet of 1 euro; after every loss he doubles the previous bet, and after every win his next bet is 1 euro. One day he brings 31 euros and decides to leave as soon as he has either lost five times in a row, won five times in a row, or run out of money before either happens.
a. What is the minimum number of plays needed to finish with 31 euros, if he leaves after five losses?
b. What is the minimum number of plays needed to finish with 31 euros, if he leaves after five wins?
c. If he leaves after five wins, what is his minimum possible final capital?