When using Pollard's kangaroo algorithm with a known public key, it's like having a warp drive that efficiently navigates through space, jumping through distances equivalent to 3.9 light years, leveraging the known structure provided by the public key.

However, if the public key were unknown, it would be akin to being in an unmapped region of space. Without this reference point, the algorithm would struggle to efficiently traverse the vast number space, much like navigating through uncharted space would require exploring the entire area.

So, in summary, the known public key acts as a mapped star system, enabling the algorithm to efficiently navigate through the vast number space of puzzle 66.