the subject is problem solving am stuck with this!!!

Alice and Bob attend a charity auction and decide to bid on the same item, a headband worn by the lead guitarist of their favorite, but not very successful, band. The rules of the auction are as follows: Alice and Bob make alternating bids. Nobody else is interested in the headband. The bid must be higher than the last bid by $10, $20 or $50. We start at $0. Alice or Bob are unwilling to pay more than $100, so whoever bids $100 wins. We can think of the auction as being a strategy game. a) Draw a state graph representing this game. Specify your notation for the graph carefully. b) Bob lets Alice go first. Making an appropriate assumption, who wins. c) How many different combinations of legal bids adding to $100 are there, what are they, and how does this relate to the state graph? d) Consider that either Alice or Bob, but not both at the same time, has only $20 notes and has to make bids of $20. Assume the other doesn't know they only have $20 notes. Does either situation change the result