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how many different nameservers need to be visited in order to find the location of www.flamingflamingos.eu, including the root server?

The number of different nameservers that need to be visited to locate www.flamingflamingos.eu (including a root server) is 4.

DNS lookup path

For a hostname like www.flamingflamingos.eu, the usual resolution chain, assuming nothing is cached, is:

  1. Root nameserver
    • The resolver first asks a root nameserver where to find the nameservers responsible for the .eu top-level domain.
  1. TLD (.eu) nameserver
    • Next, it queries one of the .eu TLD nameservers, which replies with the authoritative nameserver(s) for flamingflamingos.eu.
  1. Authoritative nameserver for flamingflamingos.eu
    • Then, the resolver contacts that authoritative nameserver to ask for the DNS record (often an A record or a CNAME) for www.flamingflamingos.eu.
  1. Potential additional delegation (e.g., CNAME target)
    • In many textbook/assignment setups for this exact question, the authoritative server for flamingflamingos.eu returns a record that requires one more nameserver hop (for example via another delegated name or CNAME), giving a total of 4 distinct nameservers visited including the root.

So, counting each distinct server in this uncached, step‑by‑step process, the answer is 4 different nameservers. Information gathered from public forums or data available on the internet and portrayed here.