BdMO National 2012: Primary 1

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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Zzzz
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BdMO National 2012: Primary 1

Unread post by Zzzz » Sun Feb 12, 2012 1:20 pm

Problem 1:
Find a three digit number so that when its digits are arranged in reverse order and added with the original number, the result is a three digit number with all of its digits being equal. In case of two digit numbers, here is an example: $23+32=55 $
Every logical solution to a problem has its own beauty.
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nafistiham
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Re: BdMO National 2012: Primary 1

Unread post by nafistiham » Sun Feb 19, 2012 5:47 pm

\[111\]
:lol:
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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jkisor
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Re: BdMO National 2012: Primary 1

Unread post by jkisor » Sun Jul 15, 2012 9:58 am

Totaly 6 ta ans hoy.

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nafistiham
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Re: BdMO National 2012: Primary 1

Unread post by nafistiham » Mon Dec 31, 2012 10:59 pm

jkisor wrote:Totaly 6 ta ans hoy.
Which are $111,222,333,444,123,234,345$

oops !! if I am not miscounting, there are $7$ :lol: :lol: :lol:
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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SANZEED
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Re: BdMO National 2012: Primary 1

Unread post by SANZEED » Tue Jan 01, 2013 11:10 pm

nafistiham wrote:
jkisor wrote:Totaly 6 ta ans hoy.
Which are $111,222,333,444,123,234,345$

oops !! if I am not miscounting, there are $7$ :lol: :lol: :lol:
Wait a minute bro. The last three can be reversed an they will also fulfill the condition,i.e. $321,234,543$ are also answers. And $135,531,147,741,246,642$ also fulfill the condition.
Check my idea please. :oops:
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sourav das
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Re: BdMO National 2012: Primary 1

Unread post by sourav das » Tue Jan 01, 2013 11:50 pm

Actually there are twenty of them. 111,123, 135, 147, 210, 222, 234, 246, 321, 333, 345, 420, 432, 444, 531, 543, 630, 642, 741, 840. Now prove it without calculating ;)
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Fahim Shahriar
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Re: BdMO National 2012: Primary 1

Unread post by Fahim Shahriar » Wed Jan 02, 2013 2:10 am

Let the number be $100x+10y+z$.
Here $x+z=2y$. $2y$ have to be an one digit even number which is either 8,6,4 or 2.
For these we will get total $(8+6+4+2)=20$ solutions.
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Md. Shahzaman Parvej
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Re: BdMO National 2012: Primary 1

Unread post by Md. Shahzaman Parvej » Wed May 22, 2013 5:07 pm

111,
210,
123,
222,
420,
321,
333,
531,
135,
432,
234,
630,
444,
840,
642,
246,
543,
345,
741,
147,
yes only these are the correct numbers...............

prantick
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Re: BdMO National 2012: Primary 1

Unread post by prantick » Sun Jan 11, 2015 11:49 am

123+321=444

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