IIT JEE , AIEEE Forum - Mathematics , Algebra - A question on combinatorics,involving a bit of chess.....

Milo_Breakin_free

Q:How many ways can we put a white and a black king on a chessboard so that they do no attack each other???

Chandravadan

I don't have much time, so i'll just tell you the method...

This has to be broken up into cases,

1. One of the kings is placed in the squares at the edges of the board but not the corners,

2.edges and corners

3. Any other place.

And work out the possibilities, Best of luck!

sboosy

Let us take the Black King.

When placed in any one of the 4 corners ,white king will have 60 other places to be placed in

Thus 60*4 = 240

When placed in any one of the side squares(ending rows but not corners)

white king will have 58 other places to be placed in

Thus 24*58 = 1392

When placed in any one of the middle squares (Excepting the ending rows)

white king will have 55 other places to be placed in

Thus 36*55 = 1980

Thus totally we have 3612 ways

No need to double it as we have already considered the possible cases

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