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The director's vacation

The director's vacation

The director of a school went on vacation to the mountains. During his vacation days the following happened:

- It rained seven times in the morning or in the afternoon.
- When it rained in the afternoon the morning was clear.
- There were exactly five clear afternoons and six clear mornings.

How many sunny days did the director enjoy?

Solution

It is clear that there were a total of 11 mornings or clear afternoons and seven in which it was raining. Since there are no more possibilities, that makes a total of 18 mornings or afternoons, that is, nine days, of which six mornings were clear and three rainy, while there were five clear and four rainy afternoons (which coincided with four mornings cleared). In summary, only two days did not rain, of the nine that was on vacation.