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# One puts two towers—white and black—on a

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SVP
Joined: 03 Feb 2003
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One puts two towers—white and black—on a [#permalink]  08 Aug 2003, 07:55
One puts two towers—white and black—on a chessboard. In how many ways can one put them, given that the towers do not kill each other?
SVP
Joined: 03 Feb 2003
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Let us wait for other people
Manager
Joined: 25 Apr 2003
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Sorry for trouble. How exactly does a tower move ?straight or diagonally ? Not much of a chess enthusiast ! notations for pieces are different you see !
SVP
Joined: 30 Oct 2003
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Location: NewJersey USA
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There 64 positions for one tower to be placed. For each postion other tower can occupy (8-1) * (8-1) postions

Total = 64*49
Senior Manager
Joined: 11 Nov 2003
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Location: Illinois
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anandnk wrote:
There 64 positions for one tower to be placed. For each postion other tower can occupy (8-1) * (8-1) postions

Total = 64*49

Hey Anand,

Are you and stolyar assuming that the two towers can be arranged only in straight lines and not diagonally?

I did this way

Number of selecting two positions on a chess board = 64C2

For each of this selection, we can arrange the two towers in 2 ways.

So the total number of ways = 64C2 * 2 = 64 X 63

What am I doing wrong? Thanks
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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Kudos [?]: 41 [0], given: 0

Select any position for the tower to be placed. Once you place the tower you cannot place another tower in any row or column that contains the postion you have chosen. So only 7 rows and 7 columns are left for you to position another tower.
Basically you lost 16 postions out of 64.
For each postion another tower can occupy 49 other postions.
so for 64 postions you have 64*49 postions.
Tower can traverse either the row or column entirely to kill another tower.
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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Kudos [?]: 0 [0], given: 0

anandnk wrote:
Select any position for the tower to be placed. Once you place the tower you cannot place another tower in any row or column that contains the postion you have chosen. So only 7 rows and 7 columns are left for you to position another tower.
Basically you lost 16 postions out of 64.
For each postion another tower can occupy 49 other postions.
so for 64 postions you have 64*49 postions.
Tower can traverse either the row or column entirely to kill another tower.

I am not sure why we have to assume the bold part in your message. It is not given in the problem. Is it the rule in chess or what? I am not really very familiar with chess.
SVP
Joined: 30 Oct 2003
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Location: NewJersey USA
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Yes sir it is the rule of chess.

Good to know that there is someone who does not know chess. I dont know how to play cards. So I dont even attempt problems with deck of cards. I am just kidding
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