Q OF SPORTS- CHESS

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Sangita - sorry
only 25 sq in chess
If both players put 16 Knights each. They need 32 SQ
There is room on chess board for 25 sqS
 
Namaskar Dudee kaka ,
32 knights can be placed on a chess board (either all on black squares or all on white squares) In this arrangement no two knights attack each other and no other square is left unattacked.
I hope this is the correct answer.
 
Shekar Beta
Good try - but no luck
I try to give you some hint by 25 sqs
32 knights can be use on board-
But be want minimum- so that every sq contains or attack by a knight ?
 
Dudee Kaka,
Minimum to phir 24 knights hain.

K K _ K K _ K K
K _ _ _ _ _ _ K
_ _ _ _ _ _ _ _
K _ _ K K _ _ K
K _ _ K K _ _ K
_ _ _ _ _ _ _ _
K _ _ _ _ _ _ K
K K _ K K _ K K

The arrangement is shown above where K = Knight and _ is an unfilled square.
No two Knights are attacking each other and no blank is left unattacked.
Ye to sahi hona chaiye.

P.S 32 is the maximum no. of knights that can be placed.
 
Dudee kaka,
Could you explain how to place 5 knights on a 8x8 chess board in a + shape.
I could not get the answer !!

Each knight can attack 2 squares in each of the four directions . Thus for a knight atmost 9 positions are occupied on the board [( 2x4directions )+(1 where he is standing)]
If 5 is the answer then maximum of 45 (9x5) squares are involved . What about the rest 19 (64-45) squares?
 
Dudeeji,

At least 12 Knights are required to occupy or attack all 64 chess board squares.

- - - - - - - -
- - K - - - - -
- - K K - K K -
- - - - - K - -
- - K - - - - -
- K K - K K - -
- - - - - K - -
- - - - - - - -

If 5 is the answer then the problem specification has to be different.

Birbal Singh
 
Dear Dr. Birbal Singh ji,

In this arrangement the Knights at positions A, B, C and D attack each other , Which should not happen as per the given problem.

_ _ _ _ _ _ _ _
_ _ K _ _ _ _ _
_ _ K A _ K K _
_ _ _ _ _ B _ _
_ _ D _ _ _ _ _
_ K K _ C K _ _
_ _ _ _ _ K _ _
_ _ _ _ _ _ _ _


Answer is surely not 5 as per given specification of the problem.
 
Dear Shekhar,

The problem specification is every square occupied or attacked by a knight. It does not state that no knight should attack each other. If no knight is allowed to attack each other than the answer will be different.

Birbal singh
 
Dear Dr. Birbal Singh ji,

I had a missconception that Knights are also not allowed to attack each other[ as is the case in N Queens Problem].Thanks for providing the correct analysis and answer to the problem.

Sir please verify that "If no knight is allowed to attack each other than the answer will be 16."
_ _ _ _ _ _ _ _
_ K K _ _ K K _
_ K K _ _ K K _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ K K _ _ K K _
_ K K _ _ K K _
_ _ _ _ _ _ _ _

With Regards

Shekhar
 
Shekhar,

Your answer is correct if no Knight is allowed to other Knight.

Birbal Singh

Shekhar Nehra (Apr 21, 2003 06:14 a.m.):
Dear Dr. Birbal Singh ji,

I had a missconception that Knights are also not allowed to attack each other[ as is the case in N Queens Problem].Thanks for providing the correct analysis and answer to the problem.

Sir please verify that "If no knight is allowed to attack each other than the answer will be 16."
_ _ _ _ _ _ _ _
_ K K _ _ K K _
_ K K _ _ K K _
_ _ _ _ _ _ _ _
_ _ _ _ _ _ _ _
_ K K _ _ K K _
_ K K _ _ K K _
_ _ _ _ _ _ _ _

With Regards

Shekhar
Click to expand...
 
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