## Placing Bishop in a chess board

For discussing Olympiad Level Combinatorics problems
samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Placing Bishop in a chess board

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

Ragib Farhat Hasan
Posts: 62
Joined: Sun Mar 30, 2014 10:40 pm

### Re: Placing Bishop in a chess board

I think the answer is 8.

thczarif
Posts: 17
Joined: Mon Sep 25, 2017 11:27 pm
Location: Dhaka,Bangladesh

### Re: Placing Bishop in a chess board

The answer is 14

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

### Re: Placing Bishop in a chess board

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

SYED ASHFAQ TASIN
Posts: 28
Joined: Thu Jun 02, 2016 6:14 pm

### Re: Placing Bishop in a chess board

The same problem for Queen gives the result 8.
I tried knight move to avoid other Queens.
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thczarif
Posts: 17
Joined: Mon Sep 25, 2017 11:27 pm
Location: Dhaka,Bangladesh

### 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

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

### Re: Placing Bishop in a chess board

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.