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title: Puzzle number of holidays

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# Puzzle number of holidays

https://twitter.com/ABCscience/status/1664392797380550658

X days total = 13 days raining + Y completely sunny days = 0 days that weren't sunny at all + 13 partially sunny days  + Y completely sunny days -----> (1)
Above is true because on days when it is raining there are either sunny afternoons or mornings, not raining all day.
Assume: ignore rain at night
Z days raining in the morning + U days raining in the afternoon = 13 days raining ----------> (2)
11 sunny mornings
12 sunny afternoons
When raining in the morning its fine in the afternoon, and vice versa
Assume fine = sunny

11 sunny mornings = X days total - Z days raining in the morning ---------> (3)
12 sunny afternoons = X days total - U days raining in the afternoon--------->(4)

Rearranging (2) gives:
Z days raining in the morning = 13 - U days raining in the afternoon

Substituting (2) into (3):
11 sunny mornings = X days total - (13 - U days  raining In the afternoon) = X - 13 + U
X = 24 - U ----------> (5)

(5)->(4)

12 = (24-U)-U => 2U = 12, U = 6

Therefore Z = 13 - 6 = 7

From (3), we have

X = 11 + Z = 11 + 7 = 18 total days

# Answer: 18 days in the holiday

Now, 

Y completely sunny days = X total days - 13 partially sunny days - 0 days not sunny at all
Y = X - 13 ----------------> (6)

Therefore,

Y = 18 - 13 = 5

