## BdIO-2012 Dhaka

Discuss everything related to IOI here. For more general or advanced topics use CS forum.

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sm.joty
Posts: 327
Joined: Thu Aug 18, 2011 12:42 am
Location: Dhaka

### BdIO-2012 Dhaka

Hey, friends here is the problem set of BdIO-2012 Dhaka. We should discuss about it.
Now everybody, try to solve it.

(N.B: If anyone think that it is not appropriate to post this. Then tell this as post that then the moderator can do something about this. But in my sense there no problem to post this.)
Attachments
BdOI Divisional.pdf
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

amlansaha
Posts: 100
Joined: Tue Feb 08, 2011 1:11 pm
Contact:

### Re: BdIO-2012 Dhaka

বাহ, ভাল কাজ করেছ জ্যোতি। ধন্যবাদ এইটা পাইলা কই?
অম্লান সাহা

sm.joty
Posts: 327
Joined: Thu Aug 18, 2011 12:42 am
Location: Dhaka

### Re: BdIO-2012 Dhaka

From Mahmud vaiya.
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

### Re: BdIO-2012 Dhaka

$3.$ Little K is writing a program to check whether two rectangles (say the are A and
B) intersect each other. Her algorithm is simple. She takes rectangle A and checks
whether each vertex of it lies within rectangle B. Is there any flaw in her
algorithm? Draw counter example if there is any. (7)
Ans :
rectangles.JPG (22.69 KiB) Viewed 2058 times
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
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### Re: BdIO-2012 Dhaka

$5.$ How many ways to arrange 6 cows and 8 donkeys in a line to take photo?
Curiously you can not distinguished a cow from other cows and you can not
distinguished a donkey from other donkeys. (5)
Ans :
$\frac{14!}{6!8!}$

$7.$ A number is written with 27 ones. Is it a multiple of 27? Prove your answer and
find the remainder. (10)
Ans :
logically,
it is divisible by $9$ when divided, the number will be divisible by $3$ because, $111111111$ is divisible by $9$ so, the residuw is $0$
analytically,
$X=\underline{1111\cdot\cdot\cdot\cdot\cdot1111}_{27}=111111111\cdot10^{18}+111111111\cdot10^9+111111111$
$\frac{X}{9}=123456791234567912345679$
which is divisible by $3$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

*Mahi*
Posts: 1175
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### Re: BdIO-2012 Dhaka

Go on @nafistiham

Use $L^AT_EX$, It makes our work a lot easier!

nafistiham
Posts: 829
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### Re: BdIO-2012 Dhaka

*Mahi* wrote:Go on @nafistiham

I am a know nothing about programming.But, in the last national i saw my name in the news paper on the $11^{th}$ place just doing some of the analyticals.must be some typo....

$8.$How many non-prime numbers$\leq 40$ which are divisible by the sum of their prime
factors? (7)
Ans :
the numbers will be $p^k$ where $p,k\in \mathbb{N}$ and $p$ is a prime
so, they are $2,4,8,16,32,3,9,27,5,25,7,11,13,17,19,23,29,31,37$
so the number is $19$

$12.$ One of the questions in this paper (both analytical and programming) has it's
mark written in binary. Can you identify it? Write the problem number. (10)
Ans :
analytical part $7,12$ and Programming Problems $4$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

novice
Posts: 31
Joined: Sun Dec 12, 2010 12:34 am

### Re: BdIO-2012 Dhaka

I am a know nothing about programming.But, in the last national i saw my name in the news paper on the $11^{th}$ place just doing some of the analyticals.must be some typo....
It was not a mistake! Just find 2/3 hours free some day and learn just how to code. The rest is up to your problem solving skills Just learn how to code with C language,from beginning to array/strings and a whole new world of problems will open up for you!