MathJax


Saturday, October 4, 2025

2025-268

Bitu is an explorer who sets out to visit the mysterious Bara-Al islands — a chain of 90 islands. Each island is connected by a few bridges. Whenever a new island was settled, its bridges were built with a preference for linking to islands that already had many connections. In this way, the Bara-Al islands grew according to Barabási–Albert Model of networks.  Still, as in any graph, there are pairs of islands that maximize the pairwise distance between islands.  These are called extreme islands.

So, he wonders: what is the expected number of bridges he would need to cross, starting from an extreme island and traveling to the farthest one by means of a shortest path?

Note 1: \(90 \approx e^{4.5}\)
Note 2: \(4.5 \approx e^{1.5}\) 

A. 8

B. 6

C. 5

D. 3

E. None of the above


Original idea by: Rodolfo Bitu

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2025-271

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