Mission Impossible

What is both possible and impossible at the same time?




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The second and last letters are the same.
The fourth second and last letter is payment.

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You are in a land where thirty men and two women were dressed in classic black and white dresses.
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You are confined in a room and given two metal rods. Out of these two rods, one is magnet and the other is the iron rod. They look starkly similar. You don't have any other metal object in the room.

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