Chittagong Secondary 2017#4
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
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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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Chittagong Secondary 2017#4
Hint
Answer
Re: Chittagong Secondary 2017#4
Sorry brother,your solution is not right .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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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Chittagong Secondary 2017#4
Akash7 wrote: ↑Wed May 02, 2018 8:03 pmWHY ?? I can put 5 knights in that boat.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 .
Re: Chittagong Secondary 2017#4
No,you can't Check practically in a real chessboard.
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Chittagong Secondary 2017#4
Can you give detailed solution?
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Chittagong Secondary 2017#4
Both of us was wrong .Akash7 wrote: ↑Wed May 02, 2018 8:03 pmSorry brother,your solution is not right .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.
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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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: Chittagong Secondary 2017#4
I have found an amazing solution here.