Suppose that there are three astronauts outside a spaceship and that they decide to play catch. All the astronauts weigh the same on Earth and are equally strong. The first astronaut throws the second one toward the third one and the game begins. Describe the motion of the astronauts as the game proceeds.

How many throws will the game last for (including the one that starts the game)?

**Details**

- Assume a 1D kinematic, purely mathematical approach (astronauts go left and right only, and don't get hungry, tired, hit by a meteor, nuked by... erm.. , rescued by aliens, etc...)
- "Equally strong" implies that they impart equal impulse when throwing one another.

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