14. Johannes told me that it rained seven times during his holiday. When it rained in the morning, it was sunny in the afternoon; when it rained in the afternoon, it was sunny in the morning. There were 5 sunny mornings and 6 sunny afternoons. Without more information, what is the least number of days that I can conclude that the holiday lasted?
A 7
B 8
C 9
D 10
E 11
14. C Let $m$ be the number of days with sunny mornings and wet afternoons. Let $n$ be the number of days with sunny mornings and sunny afternoons. There were 5 sunny mornings so $m+n=5 \ldots$ (1). Since there are seven wet days, the number of days with wet mornings and sunny afternoons must be $7-m$. There are 6 sunny afternoons so $n+(7-m)=6$, which rearranges to $m=n+1 \ldots$ (2).
Equations (1) and (2) together give $m=3, n=2$, so Johannes had 3 days with sunny mornings and wet afternoons, 2 days sunny all day, and 4 days with wet mornings and sunny afternoons, a total of 9 days (not counting any cloudy days he may have had!).