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Firstly you will need permit in advance from Kochi authorities to be allowed in Lakshadweep. Also, wherever in India you are based, you will have to go to Lakshadweep through Kochi only (even flights). In 3 nights you can cover islands like Agatti and Bangaram or thinnakara. Water activities, snorkeling, diving is pretty much done everywhere, it's the different islands one needs to stay at.
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You could try visiting Minicoy island
Bangaram island
Marine museum
Lighthouse @ Minicoy
Do a yatch cruise
Shop for handicraft, oils and spices in Kavaratti.
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One you check out the raja Reddy telugu traveller channel in YouTube he had went to Lakshadweep island by waterways
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