Snail dating game

Four snails are playing a strange dating game, one by one, the snails take off along a straight line. The snails leave \(\text{1 s}\) apart from one another with a random speed between \(\text{0}\) and \(\text{1 m/s}\), in the same direction. If two snails collide with one another, they are paired instantly, and leave the line. If they are lucky, every snail will collide a mate and live happily ever after. What is the probability that all four snails are eventually paired with a mate?

The snails can pair off in the following two ways:

Notes and assumptions

  • For simplicity, treat the snails as point particles
  • Snails are hermaphrodites, so any two snails can mate with each other

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