Hard Logic Sequence Puzzle

Complete the following series. It.s very logical:

1, 4, 5, 6, 7, 9, 11, __?




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If 21x = 79x, what is the value of x?

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I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
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A boy collects white seashells from the sea and brings them home every night. When he has enough of them, he decides to sell them to a trader.

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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 need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
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What is the best strategy?

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Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

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Artificial Intelligence has crushed all human records in the puzzle game “2048,” achieving a high score of 839,732 and beating the game in only 973 moves without using any undo.