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Tell me something only you would know.
(comicpress.socksandpuppets.com)
These situations are a great opportunity to ask your party members questions that they normally refuse to tell you about.
I think in real life, these captchas often accept your answer in both cases, in the case of ambiguity.
These captchas often don't actually have the answer included - they're collecting the answers so they can train bots in object recognition. They take your answer and compare it to a bunch of near simultaneous answers from other people, then accept it if it's close to what other people are saying.
This is true!
So to answer “Do I select one that only has its tail?”, it depends on what most people pick, so just trust your gut feeling.