When the story surfaced that President Donald Trump is considering an offer to buy Greenland, many people thought it was a joke. It came at a time when the Edinburgh fringe festival was on and almost eclipsed a joke about a vegetable regarded as the funniest this year. A Swedish comedian, named Olaf Falafel took the title with: "I keep randomly shouting out 'Broccoli' and 'Cauliflower' – I think I might have florets". Well it turns out Trump wasn't joking, he has since then confirmed his interest; it would "essentially be a large real estate deal." So why would Trump want to buy Greenland? Definitely not for a golf course as 80% of the island is under ice. Its strategic importance; it is a critical site to trace intercontinental ballistic missiles and satellites and untapped mineral resources is more likely to be the reason. Greenland's ice is melting fast and the island is thought to be rich in diamonds, gold, rubies and oil. Trump has suggested it is costing Denmark too much and perhaps he is looking for a legacy. Like many other leaders of state; he would like to achieve something which he can be remembered for. He is not the first US President who had this idea, President Harry Truman offered to buy Greenland in 1946 for $100m. After the initial amusement of the offer, Greenland said they were not for sale, but was open for business and Denmark's Prime Minister claimed the idea of selling the world's largest island was "absurd". – Linda van Tilburg.Greenlanders baffled by Trump interest.By Jason Douglas | Photographs by Christian Klindt Sølbeck for The Wall Street Journal ___STEADY_PAYWALL___.(The Wall Street Journal) NUUK, Greenland – Daniel Thorleifsen has a suggestion for President Trump: Maybe try playing golf here first before putting in a bid for Greenland.The nine-hole course Mr. Thorleifsen oversees as president of Nuuk Golf Club is open only four months a year. The rest of the time it is covered in snow. Players scramble over crags and stomp on wild berries to navigate from tee to tee while Air Greenland turboprops roar onto the airstrip nearby."He's welcome to play if he came here. But he would find it very hard," Mr. Thorleifsen said.Mr. Trump has become entranced by the idea of the US buying this vast, ice-shrouded island on the roof of the world, people familiar with discussions said. President Trump on Sunday confirmed his interest in potentially purchasing Greenland, but said it wasn't a priority. The territory's appeal seems rooted in its natural resources in addition to providing the US with another doorstep to the Arctic as the ice sheet shrinks.But the president's interest has drawn mixed reactions in Nuuk, the country's capital, a sparse city just 150 miles south of the Arctic Circle. Lapped by the Labrador Sea, its low-rise, brightly painted houses and apartment blocks are home to around a third of Greenland's 56,000 inhabitants.For some, the idea of buying and selling their homeland is a highhanded reminder of a painful and unresolved colonial legacy, which saw its indigenous inhabitants' culture and language suppressed during centuries of rule from faraway Copenhagen. Others discern in the president's apparent fascination a sign of the geo-strategic importance of the self-governing territory, which is part of the Kingdom of Denmark. Many simply see it as a joke.All insist that Greenland isn't for sale, as do its political leaders..All insist that Greenland isn't for sale. "People I know say 'no thanks,' " said Helene Elisasen."People I know say 'no thanks,' " said Helene Elisasen, as she threaded fishing lines with bait in the harbour to catch halibut at sea.Greenland is the world's largest island, covering more than 800,000 square miles in the North Atlantic and Arctic Sea northeast of Canada. It is larger than Mexico and around the same size as Saudi Arabia. Around 80% of the country is cloaked in ice, with human settlements hugging the coast. A network of airstrips and helipads, some dating from World War II, allow residents to jump from city to city in the absence of major roads.Its economy is sustained by shrimp and fish exports and a $591m annual subsidy from Denmark. Growing industries include tourism and mining. Active mines churn out rubies and minerals used to make fibre glass, and projects are under way to assess the feasibility of mining rare earths and uranium, Greenlandic officials say.The abundant resources mean any buyer for Greenland would struggle to make a fair offer for the country, said Pavia Zeeb, a fisherman. "It's too expensive," he said.Many Greenlanders like to relax by hunting caribou in the wilderness. Workplaces in Nuuk empty during the summer whenever a whale catch lands so that every household can grab a share, locals say. The raw liver of a newly killed seal is a prized delicacy..Traditional Inuit tattoo artist Maya Sialuk described the idea of the US buying Greenland as insensitive and rude.Maya Sialuk practices traditional Inuit tattooing, an ancient art her ancestors used to ward off illness and seek good fortune when hunting and fishing. She described the idea of the US buying Greenland as insensitive and rude."We are still trying to recover from a colonisation period of almost 300 years," she said. "Then there is this white dude in the States who's talking about purchasing us."Whether the president's aspiration is serious or not, Washington will continue to view Greenland as vital to American national-security interests. A decades-old defense treaty between Denmark and the US gives the US military virtually unlimited rights in Greenland at America's northernmost base, Thule Air Base, which houses part of a US ballistic missile early-warning system.Greenland's strategic importance to the US was underscored further last year when the Pentagon worked successfully to block China from financing three airports on the island. With American prodding, Denmark's government instead asked a consortium led by Danske Bank to help assemble an alternative financing package..The nine-hole course Mr. Thorleifsen oversees as president of Nuuk Golf Club is open only four months a year.In Copenhagen, which still sets Greenland's foreign and defense policies, news of Mr. Trump's enthusiasm for the territory has been interpreted as the latest signal from Washington that the US is an engaged player in the Arctic, a zone of increasing economic and strategic rivalry with both China and Russia."The US wants to make everyone aware the US is an Arctic power," said Nils Wang, a retired Royal Danish Navy rear admiral and director of Naval Team Denmark, an association for navy suppliers.Denmark, too, aims to explore new research and economic opportunities as the Arctic opens up, and has warned that Greenland will lose its annual subsidy if it pushes for independence. Mr. Trump is due to meet the Danish and Greenlandic premiers during a previously planned visit to Copenhagen next month, alongside the leader of the Faroe Islands, another autonomous Danish region..Múte Bourup Egede, leader of the left-wing, pro-independence Inuit Ataqatigiit party in Greenland's parliament.Múte Bourup Egede, leader of the left-wing, pro-independence Inuit Ataqatigiit party in Greenland's parliament, said such strategic games – and Mr. Trump's icebound fantasy – serve to remind Greenlanders of their country's outsize importance in world affairs."America will always have an interest in Greenland," said Mr. Egede, cradling a Bernie Sanders 2016 coffee mug. "Our country will always be ours."Write to Jason Douglas at jason.douglas@wsj.com