1999 Advanced Topics #2: Stacy Goes Shopping
Source:
June 21, 2012
Problem Statement
Stacy has dollars. She enters a mall with shops and a lottery stall. First she goes to the lottery and her money is doubled, then she goes into the first shop and spends dollars. After that she alternates playing the lottery and getting her money doubled (Stacy always wins) then going into a new shop and spending . When she comes out of the last shop she has no money left. What is the minimum possible value of ?