Word Order Series

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den




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Clue 3: There is no card of an ace.
Clue 4: There are no face cards (queen, king, jacks).
Clue 5: Difference between the 2nd card and 4th card is 7.

Identify four cards?

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