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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...) – arjafi 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
up vote 2 down vote accepted

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

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