Placing Bishop in a chess board

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samiul_samin
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Placing Bishop in a chess board

Unread post by samiul_samin » Thu Mar 01, 2018 5:43 pm

Prince begins to plce bishop in a chess board ($8×8$).After placing how many bishops Prince will be that on the next move at least ine bishop will attack another?
Note that
Bishop can move only diagonally and can never go to the opposite color squares.
This a simillar problem of BdMO National Higher Secondary 2014/2

Ragib Farhat Hasan
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Re: Placing Bishop in a chess board

Unread post by Ragib Farhat Hasan » Tue Aug 28, 2018 1:45 am

I think the answer is 8.

thczarif
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Re: Placing Bishop in a chess board

Unread post by thczarif » Tue Dec 04, 2018 3:20 pm

The answer is 14 :D :D

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samiul_samin
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Re: Placing Bishop in a chess board

Unread post by samiul_samin » Thu Jan 10, 2019 12:17 am

thczarif wrote:
Tue Dec 04, 2018 3:20 pm
The answer is 14 :D :D
Can you please post the full solution?

SYED ASHFAQ TASIN
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Re: Placing Bishop in a chess board

Unread post by SYED ASHFAQ TASIN » Thu Feb 21, 2019 5:19 pm

The same problem for Queen gives the result 8.
I tried knight move to avoid other Queens.
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thczarif
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Re: Placing Bishop in a chess board

Unread post by thczarif » Thu Feb 21, 2019 5:46 pm

As bishops in the black squares don't attack the bishops on the white squares so, we can count at most how many bishops we can place on the white squares and then double the number to get the total.
Now, lets divide the chess board into 8 white diagonals. We can place 8 bishops in those but we can't put two of them on the same long diagonal so we can put at most 7 bishops on the white squares and which is possible so we can put at most 7*2=14 bishops

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samiul_samin
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Re: Placing Bishop in a chess board

Unread post by samiul_samin » Thu Feb 21, 2019 7:39 pm

SYED ASHFAQ TASIN wrote:
Thu Feb 21, 2019 5:19 pm
The same problem for Queen gives the result 8.
I tried knight move to avoid other Queens.
The same problem of $ROOK$ gives the result $8$ .
I placed the $ROOKS$ diagonally. :D :) :)

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