# Number of days it took to climb the mountain (BdMO 2012 National Primary/Junior question)

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.

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Contradictory tags? –  Jp McCarthy Jun 14 '13 at 8:16
@Jp McCarthy,I was not exactly sure what to tag it with. –  rah4927 Jun 14 '13 at 8:16
@JpMcCarthy: I find elementary set theory quite recreational. ;-) (Oh, you meant...) –  Arthur Fischer Jun 14 '13 at 8:17
Well, wouldn't it be 3x it rained in the afternoon, leaving 8 rainy days, for each you see a morning or an afternoon, so its 9 sunshine days. 9 afternoons, 9 mornings, 4 rainy afternoons, 4 shiny mornings, 4 rainy mornings, 4 shiny afternoons, 3 rainy afternoons, 3 shiny afternoons. Thats 11 rainy days, and 9 sunshine days, resulting in a 20 day journey. –  SinisterMJ Jun 14 '13 at 8:21
@Arthur Fischer,I got it from the junior section of the nationals.Did not know it came in the primary section as well. –  rah4927 Jun 14 '13 at 8:26

I'll approach it up front:

Every day is divided in 2 sections:

• morning or rain

• afternoon or rain

Since it says that it can only rain once in a day, it doesn't even need to be accounted for a full day rain, so the number of days is

mornings$+$ afternoons $+$ rainy times $=$ 2 $\times$ amount of days

Thus $16 + 13 + 11 = 2$ $\times$ days -> days = 20 And it fits: 9 sunshine days, 7 morning sunshine, 4 afternoon sunshines.

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Thanks for the answer.I was getting answers like 23,24 from others . –  rah4927 Jun 14 '13 at 8:30