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1.Its capital is on the Atlantic coast
Gabon
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Peru
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Libreville is an Atlantic city, Lima is a Pacific city.
2.Its official name in English is "Republic of __________"
Gabon
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Peru
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Gabonese Republic ("République gabonaise") vs. Republic of Peru ("República del Peru")
3.Its most-used language is Spanish
Gabon
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Peru
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Gabon: French; Peru: Spanish
4.It does not touch the equator
Gabon
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Peru
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Peru comes within 5km of the equator, but does not touch it.
5.It is in the southern half of its continent (South America vs. Africa)
Gabon
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Peru
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Taking measurements from the extreme north of Colombia to the extreme south of Chile, Peru is in the northern half of South America. In the same way, Tunisia - South Africa, Gabon is [just] entirely in the southern half.
8.It shares a currency with neighbouring countries
Gabon
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Peru
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Gabon uses the Central African Franc, along with Cameroon, C.A.R., Chad, R.O.C. and Equatorial Guinea. Peru uses its own currency, the Sol.
9.It has had a citizen serve as UN Secretary General
Gabon
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Peru
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Peruvian Javier Pérez de Cuéllar served as UN Secretary General 1982-1991.
10.It has a higher GDP per capita
Gabon
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Peru
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Gabon: $19,252; Peru: $13,410
11.It has more forest coverage (% of area)
Gabon
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Peru
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Gabon: 89.3%; Peru: ≈60% (not easy to calculate, but pretty clear that Gabon is "ahead")
12.Its flag has horizontal stripes
Gabon
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Peru
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Gabon: horizontal green, yellow, blue stripes; Peru: vertical red and white stripes
13.It has a higher population density
Gabon
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Peru
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Gabon: 8/km squared; Peru: 24/km squared
14.Its exports are dominated by petroleum
Gabon
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Peru
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Peru's exports are dominated by metal ore, although petroleum is also a major part. Gabon's exports are massively dominated by petroleum.
15.Its capital city is closer to Tokyo
Gabon
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Peru
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Libreville-Tokyo: Cross Africa, cross the Arabian Sea, cross India & China, then cross the sea to get to Japan. It is still a shorter distance than Lima-Tokyo, crossing the Pacific ocean.
Haha, well I started with Peru because I live there and my imagination isn't all that enormous, but Gabon? Hard to say, I wanted a country that was as different as possible without being ridiculously different, if that makes sense.