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Corrine was looking at the weather forecast and it said it was going to rain for 12 days straight.
When it did rain in the AM the PM was clear, and when it rained in the PM the AM was clear.
Overall the weather was clear 9 days in the AM and 11 days in the PM.
How many of those day was the weather clear for Corrine all day?
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Unfortunately, in the form presented in the post, the problem is SELF-CONTRADICTORY and makes no sense.
But it can be fixed, if edited, replacing 12 days straight by 21 days straight, as it SHOULD BE.
Below is my editing and the solution for the edited version.
Corrine was looking at the weather forecast and it said it was going to rain for days straight.
When it did rain in the AM the PM was clear, and when it rained in the PM the AM was clear.
Overall the weather was clear 9 days in the AM and 11 days in the PM.
How many of those was the weather clear for Corrine all day?
S O L U T I O N
Let A be the subset of the 21 days with raining in the AM, and let P be the subset of the 21 days with raining in the PM.
According to the problem, these subsets are disjoint (have empty intersection).
Therefore, the total number of days raining is 9 + 11 = 20.
Hence, only one day of the 21 days straight was clear all the day.
Edited and solved completely, with comprehensive explanations.
My editing turned out this problem from nonsense into the sparkling diamond.