Let's say we get $20000$ circles with random centers in a $200\times200$ square centered at the origin, with radii uniformly distributed over ${1,2,...,200}$. Call a circle "nested" in another if the first circle completely contains the second. What is the expected length of the largest "nesting" of all circles? Put another way, what is the longest chain of circles within circles you can expect?
2026-04-01 03:06:59.1775012819
Predicting the number of nested circles
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