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### Placing Bishop in a chess board

Posted: **Thu Mar 01, 2018 5:43 pm**

by **samiul_samin**

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

This a simillar problem of BdMO National Higher Secondary 2014/2

### Re: Placing Bishop in a chess board

Posted: **Tue Aug 28, 2018 1:45 am**

by **Ragib Farhat Hasan**

I think the answer is 8.

### Re: Placing Bishop in a chess board

Posted: **Tue Dec 04, 2018 3:20 pm**

by **thczarif**

The answer is 14

### Re: Placing Bishop in a chess board

Posted: **Thu Jan 10, 2019 12:17 am**

by **samiul_samin**

thczarif wrote: ↑Tue Dec 04, 2018 3:20 pm

The answer is 14

Can you please post the full solution?

### Re: Placing Bishop in a chess board

Posted: **Thu Feb 21, 2019 5:19 pm**

by **SYED ASHFAQ TASIN**

The same problem for Queen gives the result 8.

I tried knight move to avoid other Queens.

### Re: Placing Bishop in a chess board

Posted: **Thu Feb 21, 2019 5:46 pm**

by **thczarif**

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

### Re: Placing Bishop in a chess board

Posted: **Thu Feb 21, 2019 7:39 pm**

by **samiul_samin**

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.