## BdMO National 2012: Secondary 2, Junior 3, Primary 7

Zzzz
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### BdMO National 2012: Secondary 2, Junior 3, Primary 7

Problem:
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?
Every logical solution to a problem has its own beauty.

nafistiham
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

একটি ছোট সমাধানঃ
এটা আমার এক পরিচিতের সমাধান । আমার উত্তর আসছিল ২৪ দিন
[কান্না পাচ্ছে । ]
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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Abid
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

আমি করসি বিশাল সমাধান......... সেট দিএ...।। :\

nafistiham
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

solution using sets is obviously a rigourous one.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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Abdul Muntakim Rafi
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

Tiham: it never rains twice in the same day... So I think 24 days...
Man himself is the master of his fate...

nafistiham
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

Abdul Muntakim Rafi wrote:Tiham: it never rains twice in the same day... So I think 24 days...
ভাইয়া, $২৪$ দিন হলে বেশি গোনা হয়ে যায় । আমিও ওই ভুলটাই করেছিলাম ।
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

Tashin
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

উত্তরঃ হল ২৪।
২৪ দিন হলে মোট ২৪ টি সকাল + ২৪ টি বিকেল
বৃষ্টি বিহীন সকাল ১৬ টি বাদ দিলে (২৪-১৬)= ৮ টি সকাল থাকে বৃষ্টি হওয়ার জন্য।
বৃষ্টি বিহীন বিকেল ১৩ টি বাদ দিলে(২৪-১৩)=১১ টি বিকেল বৃষ্টি হওয়ার জন্য।
তাহলে, ৮ টি সকাল ও (১১-৮)=৩ (*) টি বিকেলে ,মোট ১১ দিন বৃষ্টি হয়।
*(যেদিন সকালে বৃষ্টি হয় ঐ দিন বিকেলে হয় না)

sakib.creza
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### Re: BdMO National 2012: Secondary 2, Junior 3, Primary 7

Total (16+13)=29 times it didn't rain. total 11 times it rained. So in total there were (29+11)=40 times he was up there. So for (40/2)=20 days he was up there.
It either rained or it didn't rain. No other possibilities exist. 24 days mean 48 times. But only 40 times are stated about in the question.