## Chittagong Secondary 2017#4

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- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

### Chittagong Secondary 2017#4

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

- samiul_samin
**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.

- samiul_samin
**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.

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: Chittagong Secondary 2017#4

Can you give detailed solution?

- samiul_samin
**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 $503×4 +4=2016$

- samiul_samin
**Posts:**1007**Joined:**Sat Dec 09, 2017 1:32 pm

### Re: Chittagong Secondary 2017#4

I have found an amazing solution here.