## BdMO National 2012: Primary 1

Zzzz
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### BdMO National 2012: Primary 1

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.

nafistiham
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### Re: BdMO National 2012: Primary 1

$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

jkisor
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### Re: BdMO National 2012: Primary 1

Totaly 6 ta ans hoy.

nafistiham
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### Re: BdMO National 2012: Primary 1

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

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

SANZEED
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### Re: BdMO National 2012: Primary 1

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 $7$
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.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

sourav das
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### Re: BdMO National 2012: Primary 1

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
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

Fahim Shahriar
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### Re: BdMO National 2012: Primary 1

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.
Name: Fahim Shahriar Shakkhor
Notre Dame College

Md. Shahzaman Parvej
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### Re: BdMO National 2012: Primary 1

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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