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Placing Bishop in a chess board
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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?
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This a simillar problem of BdMO National Higher Secondary 2014/2
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Re: Placing Bishop in a chess board
I think the answer is 8.
Re: Placing Bishop in a chess board
The answer is 14
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Re: Placing Bishop in a chess board
The same problem for Queen gives the result 8.
I tried knight move to avoid other Queens.
I tried knight move to avoid other Queens.
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Re: Placing Bishop in a chess board
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
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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Re: Placing Bishop in a chess board
The same problem of $ROOK$ gives the result $8$ .SYED ASHFAQ TASIN wrote: ↑Thu Feb 21, 2019 5:19 pmThe same problem for Queen gives the result 8.
I tried knight move to avoid other Queens.
I placed the $ROOKS$ diagonally.