BdMO National Higher Secondary 2014/2

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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samiul_samin
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BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 6:24 pm

Closing his eyes Tawsif begins to plca knights on a Chess board of $21\times 23$.After plcing how many knights Tawsif will be sure that in next move at least one knight will attack another one?

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 6:26 pm

Hint
Think about smaller boards.
Answer
$\fbox {242}$
Last edited by samiul_samin on Sun Feb 18, 2018 7:03 pm, edited 1 time in total.

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 6:27 pm

Simillar problem
BdMO National Secondary 2014/3
Last edited by samiul_samin on Sun Feb 18, 2018 7:46 pm, edited 1 time in total.

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 7:09 pm

Chess Knowing basic Chess rules is better to solve this problem.It is really an interesting problem which is also important for programmers!

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ahmedittihad
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Re: BdMO National Higher Secondary 2014/2

Unread post by ahmedittihad » Sun Feb 18, 2018 7:43 pm

Do not spam in the forum.
Frankly, my dear, I don't give a damn.

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 7:47 pm

ahmedittihad wrote:
Sun Feb 18, 2018 7:43 pm
Do not spam in the forum.
What do you mean?

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Re: BdMO National Higher Secondary 2014/2

Unread post by ahmedittihad » Sun Feb 18, 2018 7:49 pm

What I mean is, you have posted 4 posts which you could have done in 1. That's spamming.
Frankly, my dear, I don't give a damn.

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 7:51 pm

ahmedittihad wrote:
Sun Feb 18, 2018 7:49 pm
What I mean is, you have posted 4 posts which you could have done in 1. That's spamming.
Oh,Sorry.I don't know it.I am really sorry.I will not do it later. :| :cry: :cry: :cry:

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samiul_samin
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Re: BdMO National Higher Secondary 2014/2

Unread post by samiul_samin » Sun Feb 18, 2018 8:18 pm

Here is the detailed Solution
Step 1.Making $21×23$ chess board
First,think about $22×22$ chess board .There are $484$ squares.Half of them are black and half of them are white.You can cut any file of it.Then,you have $21×22 $ chessboard.You cancelled $11 $white squares and $11$ black squares.So,there are $231$ black squares and $231$ white squares.In any side file of $21×22$ chessboard you will get two white squares.Now,add a new file of $21 $square with it where the two corner squares of it is obviously black(followed by the last line).So,in this new line there are $11$ black squares and $10$ white squares.
So,in this new $21×23$ chess board there are,$
231+11=242$ black squares and $
231+10=241$ white squares.
Step 2. Putting Knights
Now,put knights in every black squares.None of them will attack any other knights.Because,knight placed in a black square can attack only pieces which are placed in white square.But,there is no knights in white squares.So,putting knight is completed.
Step 3. Justify the highest number
But if Tawsif puts another one,it should be placed in a white square and it is sure that the last knight will be attacked by other knight.
So,the highest number of knights is $\fbox {242}$

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