Problem: 51st state:

There are four categories of terra nullius, land that is unclaimed by any state: the small unclaimed territory of Bir Tawil between Egypt and Sudan, Antarctica, the oceans, and celestial bodies such as the Moon or Mars. In the last three of these, international treaties (the Antarctic Treaty, the United Nations Convention on the Law of the Sea, and the Outer Space Treaty respectively) prevent colonization and potential statehood of any of these uninhabited (and, given current technology, not permanently inhabitable) territories.

Where is Bir Tawil located?
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A: between Egypt and Sudan

Problem: Pain:

In his book, The Greatest Show on Earth: The Evidence for Evolution, biologist Richard Dawkins grapples with the question of why pain has to be so very painful. He describes the alternative as a simple, mental raising of a "red flag". To argue why that red flag might be insufficient, Dawkins explains that drives must compete with each other within living beings. The most fit creature would be the one whose pains are well balanced. Those pains which mean certain death when ignored will become the most powerfully felt. The relative intensities of pain, then, may resemble the relative importance of that risk to our ancestors (lack of food, too much cold, or serious injuries are felt as agony, whereas minor damage is felt as mere discomfort). This resemblance will not be perfect, however, because natural selection can be a poor designer. The result is often glitches in animals, including supernormal stimuli. Such glitches help explain pains which are not, or at least no longer directly adaptive (e.g. perhaps some forms of toothache, or injury to fingernails).

What does Dawkins explain must compete with each other in living begins?
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A: drives

Problem: Tuvalu:

In 1892 Captain Davis of the HMS Royalist reported on trading activities and traders on each of the islands visited. Captain Davis identified the following traders in the Ellice Group: Edmund Duffy (Nanumea); Jack Buckland (Niutao); Harry Nitz (Vaitupu); John (also known as Jack) O'Brien (Funafuti); Alfred Restieaux and Emile Fenisot (Nukufetau); and Martin Kleis (Nui). During this time, the greatest number of palagi traders lived on the atolls, acting as agents for the trading companies. Some islands would have competing traders while dryer islands might only have a single trader.

What did palagi traders act as for the trading companies?
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A: agents

Problem: American Idol:

In May 2005, Carrie Underwood was announced the winner, with Bice the runner-up. Both Underwood and Bice released the coronation song "Inside Your Heaven". Underwood has since sold 65 million records worldwide, and become the most successful Idol contestant in the U.S., selling over 14 million albums copies in the U.S. and has more Underwood has won seven Grammy Awards, the most Grammys by an "American Idol" alumnus.

When was the winner declared?
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A:
May 2005