# Chess Probability

#### lcherry13

##### New member
Original question: How many ways are there to arrange three indistinguishable rooks on a 6 × 6 board such that no two rooks are attacking each other? (Two rooks are attacking each other if and only if they are in the same row or the same column.)

Questions wanted answered: How many ways are there to arrange three indistinguishable bishops on a 6 × 6 board such that no two bishops are attacking each other? (Two bishops are attacking each other if and only if they are in the same diagonal.)
And
How many ways are there to arrange three indistinguishable queens on a 6 × 6 board such that no two queens are attacking each other? (Queens can attack each other in any way except for the knight or L shape)

#### Subhotosh Khan

##### Super Moderator
Staff member
Original question: How many ways are there to arrange three indistinguishable rooks on a 6 × 6 board such that no two rooks are attacking each other? (Two rooks are attacking each other if and only if they are in the same row or the same column.)

Questions wanted answered: How many ways are there to arrange three indistinguishable bishops on a 6 × 6 board such that no two bishops are attacking each other? (Two bishops are attacking each other if and only if they are in the same diagonal.)
And
How many ways are there to arrange three indistinguishable queens on a 6 × 6 board such that no two queens are attacking each other? (Queens can attack each other in any way except for the knight or L shape)

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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#### pka

##### Elite Member
Original question: How many ways are there to arrange three indistinguishable rooks on a 6 × 6 board such that no two rooks are attacking each other? (Two rooks are attacking each other if and only if they are in the same row or the same column.)

Questions wanted answered: How many ways are there to arrange three indistinguishable bishops on a 6 × 6 board such that no two bishops are attacking each other? (Two bishops are attacking each other if and only if they are in the same diagonal.)
And
How many ways are there to arrange three indistinguishable queens on a 6 × 6 board such that no two queens are attacking each other? (Queens can attack each other in any way except for the knight or L shape)
Two rooks can attack one another if they are in the same row or same column.
Place a rook on the board anywhere. One row and one column are eliminated, leaving 49 spaces. WHY?

#### lookagain

##### Senior Member
Original question: How many ways are there to arrange three indistinguishable rooks on a 6 × 6 board ...
Two rooks can attack one another if they are in the same row or same column.
Place a rook on the board anywhere. One row and one column are eliminated, leaving 49 spaces. WHY?
Icherry13 is not working with the standard 8 by 8 board.

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#### pka

##### Elite Member
Icherry13 is not working with the standard 8 by 8 board.
That makes a stupid question.

#### pka

##### Elite Member
Who cares anyway!
All Pka needed to add is:
Example, using a 8 by 8 board.
No one cares if he/she is not interested in publishing. But the near universal rule in testing is: if a common setting is used do not change the particulars. That is, here chess pieces are used so don't change the size of the board. If you talk about poker or bridge, use a standard deck of cards. The reason being, most people read quickly, particularly in a testing, and tend to make certain assumptions. Further the argument goes: "noting but confusion can be added by making an unusual change". Absolutely no additional concepts can be taught or tested by changing the usual 8x8 board to a 6x6.