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There is no correct answer for the number of countries in the world. I'd recommend this Map Men video on the difficulty of deciding what is or isn't a country: https://www.youtube.com/watch?v=3nB688xBYdY
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There are some databases including territories and stuff that sometimes lands in the ~250 region, but should be stated if so. Closer to 200-210 or UNs "193 countries" tend to be a bit more common to use though, always depend on what exactly you see as a "country" I suppose.
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There are 249 country codes, which is a possible definition used.
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Out of the gate, Canada and the US share 1 as country code and includes entities that aren't countries like Globalstar (Mobile Satellite Service):

https://en.wikipedia.org/wiki/List_of_telephone_country_code...

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