### Chittagong Secondary 2017#4

Posted:

**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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Posted: **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?

Posted: **Sat Feb 24, 2018 1:53 am**

Posted: **Wed May 02, 2018 8:03 pm**

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.

Posted: **Thu May 24, 2018 11:57 am**

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 .

Posted: **Sun May 27, 2018 4:15 pm**

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

Posted: **Wed May 30, 2018 3:03 pm**

Can you give detailed solution?

Posted: **Fri Jan 11, 2019 12:00 pm**

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 $503×4 +4=2016$

Posted: **Sat Mar 09, 2019 8:01 pm**

I have found an amazing solution here.