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The weather during my vacation was as follows:

  • It was cloudy on 13 different days, but it was never cloudy for an entire day

  • Cloudy mornings were followed by clear afternoons

  • Cloudy afternoons were preceded by clear mornings

  • There were 11 clear mornings and 12 clear afternoons in all

In days, how long was my vacation?

Note: Please explain your logic.

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    $\begingroup$ Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it. If not, some responses to the answerers to help steer them in the right direction would be helpful. In particular, knowing if the lateral-thinking tag is really appropriate here would be useful; given the straightforward path to valid looking solutions, it seems out of place. $\endgroup$ – Rubio♦ Jan 11 '18 at 5:16
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I think this explains that the total vacation is

18 days:
enter image description here

Because -

Number of cloudy mornings = A
Number of cloudy afternoons = B
Number of clear days = C

Number of cloudy days = A + B = 13
Number of clear mornings = B + C = 11
Number of clear afternoons = A + C = 12

We add both sides to get 2A + 2B + 2C = 36
Total vacation length: A + B + C = 18

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I'm seeing a disappointing lack in "lateral thinking" in any of the answers so far, despite the puzzle's tag plainly telling us that the correct answer will require us to think outside the box, so I'm just going to put this here.

The duration of your vacation was:

3,285,000,000,018 days.

This is because:

You are God, and after setting off the Big Bang you decided to take a well-deserved vacation. From the time of the Big Bang, it took nine billion years for the Earth to form and have an atmosphere which was then capable of being either clear or cloudy.

Nine billion years is 3,285,000,000,000 days. The remaining 18 days cover the final few days of your vacation, during which there could finally be weather for you to enjoy (as derived in all the other answers)

I hope your vacation was a restful one, O Lord!

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Answer:

18

Explanation:

It was cloudy on 13 different days i.e. 13 total cloudy mornings/afternoons and none of them occurred on the same day.
Logically we can say that:

  • 6 clear mornings were followed by 6 cloudy afternoons.

  • 7 clear afternoons preceded by 7 cloudy mornings.

    • (Because same number of clear mornings/afternoons should be left and both must sum upto 13).

  • 5 days were all clear.

And they all sum upto 18 days.

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  • $\begingroup$ I will be really mad, if my answer isn't accepted. There was no algebra tag on this question initially. $\endgroup$ – prog_SAHIL Jan 1 '18 at 16:05
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18 Days

x: cloudy mornings   clear  afternoons
y: clear  mornings   cloudy afternoons
z: clear days

x + y = 13  (1) cloudy days
y + z = 11  (2) clear mornings
x + z = 12  (3) clear afternoons

x + y = 13  (1)
x - y = 1   (3-2)
x + z = 12  (3)

2x    = 14  (1)+(3-2)
x + y = 13  (1)
x + z = 12  (3)

x = 7       ((1)+(3-2)) / 2
y = 6       put x in (1)
z = 5       put x in (3)

x+y+z = 18 Days

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The answer:

18.

Because:

There are 36 (13+12+11) morning and afternoons in total, making 18 days.

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