From the Bangladesh Mathematical Olympiad 2012 National Secondary (Question 7, or ৭).
When Tanvir climbed the Tajingdong mountain, on his way to the top he saw it was raining $11$ times. At Tajindong, on a rainy day, it rains either in the morning or in the afternoon; but it never rains twice in the same day. On his way, Tanvir spent $16$ mornings and $13$ afternoons without rain. How many days did it take for Tanvir to climb the Tajindong mountain in total?
I tried to solve it using sets but it has not worked out too well. I asked people who did it but most of them gave different answers ,often having a difference of $1$ or $2$. Any help will be appreciated.