Alice, Ben, and Carl collect stamps. They exchange stamps among themselves according to the following scheme: Alice gives Ben as many stamps as Ben has and Carl as many stamps as Carl has. After that,...

Alice, Ben, and Carl collect stamps. They exchange stamps among themselves according to the following scheme: Alice gives Ben as many stamps as Ben has and Carl as many stamps as Carl has. After that, Ben gives Alice and Carl as many stamps as each of them has, and then Carl gives Alice and Ben as many stamps as each has.
If each finally has 64 stamps, how many stamps does Alice have at the start?

Note: Solve the problem following
Polya’s Four Step Method.