Chittagong Secondary 2017#4

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samiul_samin
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Chittagong Secondary 2017#4

Unread post by samiul_samin » Sat Feb 24, 2018 1:52 am

In a $2015×2$ chess board,what is the maximum number of horses we can put such that no horses attack each other?

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samiul_samin
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Re: Chittagong Secondary 2017#4

Unread post by samiul_samin » Sat Feb 24, 2018 1:53 am

Hint
There are $2015$ black squares in that chess board
Answer
$2015$

Akash7
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Re: Chittagong Secondary 2017#4

Unread post by Akash7 » Wed May 02, 2018 8:03 pm

samiul_samin wrote:
Sat Feb 24, 2018 1:53 am
Hint
There are $2015$ black squares in that chess board
Answer
$2015$
Sorry brother,your solution is not right :oops: :!: .It doesn't mean that if there are 2015 black squares then there can be placed 2015 horses at the maximum rate.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard such that no horse attack each other.Then add up 403 such chessboards to get a 2015*2 chessboard.So you can put at most 403*4=1612 horses in 2015*2 chessboard which meets the given condition.

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samiul_samin
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Re: Chittagong Secondary 2017#4

Unread post by samiul_samin » Thu May 24, 2018 11:57 am

Akash7 wrote:
Wed May 02, 2018 8:03 pm
samiul_samin wrote:
Sat Feb 24, 2018 1:53 am
.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard .
WHY ?? I can put 5 knights in that boat.

Akash7
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Re: Chittagong Secondary 2017#4

Unread post by Akash7 » Sun May 27, 2018 4:15 pm

No,you can't :!: Check practically in a real chessboard.

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samiul_samin
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Re: Chittagong Secondary 2017#4

Unread post by samiul_samin » Wed May 30, 2018 3:03 pm

Can you give detailed solution?

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samiul_samin
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Re: Chittagong Secondary 2017#4

Unread post by samiul_samin » Fri Jan 11, 2019 12:00 pm

Akash7 wrote:
Wed May 02, 2018 8:03 pm
samiul_samin wrote:
Sat Feb 24, 2018 1:53 am
Hint
There are $2015$ black squares in that chess board
Answer
$2015$
Sorry brother,your solution is not right :oops: :!: .It doesn't mean that if there are 2015 black squares then there can be placed 2015 horses at the maximum rate.First think about 5*2 chessboard.You can put at most 4 horses in 5*2 chessboard such that no horse attack each other.Then add up 403 such chessboards to get a 2015*2 chessboard.So you can put at most 403*4=1612 horses in 2015*2 chessboard which meets the given condition.
Both of us was wrong .
Correct answer is $2016$
As this is $n×2$ sized chess board it is a special case.
In a $4×2$ chess board I can put $4$ knights.
There are such$503$ chess bords.
Then we can put mor $4$ horses.
So,total is $503×4 +4=2016$

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samiul_samin
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Re: Chittagong Secondary 2017#4

Unread post by samiul_samin » Sat Mar 09, 2019 8:01 pm

I have found an amazing solution here.

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