1. The Naming of the Cook Islands
Captain James Cook only landed on Palmerston in the Cook Islands and named the islands the Hervey Islands. The Cook Islands name was given by the Russian explorer and map-maker, Adam Johann Von Krusenstern who fan-boyed Cook. In recent years there has been debate about returning to an original name...something like Avaiki Nui but that didn't go ahead as tourism is 75% of GDP and most Cook Islanders agreed that it would be confusing for future travellers.
https://www.rnz.co.nz/international/pacific-news/420385/renewed-calls-for-the-cook-islands-to-take-on-indigenous-name

2. The Height of Buildings Rules and Foreign Ownership Rules
Building height restrictions are based on the height of typical coconut trees over here. The tallest buildings are a few government and business 3-story ones in town. Foreign investment and ownership are strictly controlled here. That's why we have no Subway, KFC (Cookies crying) or McDonalds. All foreign investors (that's Kiwi's as well) purchase a land lease starting at 60 years and working backwards. The rest of the world could learn from the Cook Islands with this policy.

3. Special Cook Islands Currency
While the Cook Islands uses the NZ dollar, it does have its own currency, including the unusual triangle $2 coin and dodecagon $5 coin. Keep an eye out for a special $3 note of a barechested woman riding a shark. This banknote depicts the legend of Ina and the Shark. It's worth keeping if you find one :-)


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