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Rooks on a chessboard (Posted on 2018-11-26) Difficulty: 2 of 5
How many ways are there to place two rooks on the same column or same row on a nxn chessboard?

See The Solution Submitted by Ady TZIDON    
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soln attempt | Comment 1 of 4
2 n n (n-1)/2 = n^3 - n^2, no?

Logic:

Rows and columns are completely independent and identical, so find answer for rows and double it. 
There are n rows, completely independent and identical, so find solution for a row and multiple by n. 
In a row place the first rook in any of n squares and the second in any of n-1 squares: n (n-1). But you have counted each situation twice, so divide by 2.

  Posted by Steven Lord on 2018-11-26 09:50:32
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