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 $
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
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: BdMO National 2012: Primary 1
Totaly 6 ta ans hoy.
- nafistiham
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Re: BdMO National 2012: Primary 1
Which are $111,222,333,444,123,234,345$jkisor wrote:Totaly 6 ta ans hoy.
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.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: BdMO National 2012: Primary 1
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.nafistiham wrote:Which are $111,222,333,444,123,234,345$jkisor wrote:Totaly 6 ta ans hoy.
oops !! if I am not miscounting, there are $7$
Check my idea please.
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$
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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......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
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.
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
Notre Dame College
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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...............
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...............
Re: BdMO National 2012: Primary 1
123+321=444