Birthdate together

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?




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I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
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I am dry when I go inside, but wet when I am pulled outside.
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How can you make the following equation true by drawing only one straight line: 5+5+5=550 ?

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Challenging

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