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The general principle of this question is "If you could only speak n languages, which languages would those be to maximize the number of people that you could speak to?"

For example, if n = 1, then the best language would be whatever language was spoken by the most people: Mandarin Chinese.

If n = 2, it gets a little more interesting because now you need to account for the overlap between speakers of different languages. The 2nd most spoken language is Spanish but there are some people in the world who speak both Chinese and Spanish and so learning Spanish wouldn't allow you to speak with them. My guess is that the number of Spanish-Chinese speakers is relatively low and so for n = 2 your best bet is going to be Chinese and Spanish.

You get the idea by now, if I was going to speak 3 languages, it probably still follows the most spoken language trend, but at some point it will stop. Is anyone aware of a similar list of languages that takes into account the number of people that knowing that language allows you to speak to and not just the number of people that speak that language?

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I think it may be necessary to design a path that takes into account the development of language acquisition skills. There might be two different approaches to doing this the most efficient way. If the person seeking to follow such a path is naturally talented in language learning, it is probably best for them to learn a non-Indo-European language (assuming L1 or dominant English) as their L2 so as to develop their language acquisition skills quickly and to a high degree and diversify their phoneme bank early. This could be thought of as some sort of shock therapy.

If the person is not so fortunate as to be endowed with preternatural word-sponging abilities, then it may be wiser to take a gentler path toward language acquisition skill development, starting with those languages which share structural similarities or common roots with the L1, and gradually introducing more and more difficult languages until the learner is comfortable with the process of acquiring languages.

Of course, the original post's principle still stands, but this additional parameter is a consideration that could greatly benefit the learner.

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