1. With trains and ships, today's detectives move fast.

2. By trains and ships, today's detectives move fast.

3. By train and ship, today's detectives move fast.
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I can find Sentence 1 in the book "Around the World in Eighty Days."

What about Sentence 2 and 3? Which one is correct?

All are correct.

To determine which sentence is correct, we need to assess the use of articles and the singular/plural form of the nouns in the sentence.

Sentence 1: "With trains and ships, today's detectives move fast."
This sentence uses the plural form of the nouns, "trains" and "ships," and the preposition "with" to indicate the means by which today's detectives move fast. This sentence suggests that detectives have access to multiple trains and ships for their expeditions.

Sentence 2: "By trains and ships, today's detectives move fast."
This sentence also uses the plural form of the nouns, "trains" and "ships," and the preposition "by" to indicate the means of transportation. This sentence conveys the same meaning as Sentence 1 and suggests that today's detectives use multiple trains and ships for their fast movement.

Sentence 3: "By train and ship, today's detectives move fast."
This sentence uses the singular forms of the nouns, "train" and "ship," and the preposition "by" to indicate the means of transportation. This sentence suggests that today's detectives use a single train and a single ship for their fast movement.

Between Sentence 2 and Sentence 3, the correct sentence would depend on the intended meaning. If you want to convey that detectives use multiple trains and ships, Sentence 2 would be appropriate. However, if you want to emphasize the use of a single train and a single ship, Sentence 3 would be more suitable.

Considering Sentence 1, it does not appear to be related to the question you asked about Sentence 2 and Sentence 3. "Around the World in Eighty Days" is a famous adventure novel by Jules Verne but does not provide relevance to the correct usage of articles and nouns in the given sentences.