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An immortal snail is at one end of a perfect rubber band with a length of 1km. Every day, it travels 10cm in a random direction, forwards or backwards on the rubber band. Every night, the rubber band gets stretched uniformly by 1km. As an example, during the first day the snail might advance to x=10cm, then the rubber band gets stretched by a factor of 2, so the snail is now at x=20cm on a rubber band of 2km.

The challenge: Approximate the probability that it will reach the other side at some point (better approximations are obviously preferred, but any bounds are acceptable as long as they are found by doing something interesting)

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# Challenge 7b: A Snail's Pace

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