Fun in common

What does an Island and the letter T have in common?




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Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
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They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

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2, 3, 5, 9, 17, _ What is the next number in the sequence?

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Amazing Facts

Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.