rooks and squares

pascal roca

  1. How many different ways to arrange rooks on chess board knowing the condition that none of rook should lie on a square which is controlled by an other one  ?
  2. The first solution which comes up immediately is to put all the rooks on the principal diagonal
  3. then if you choose the first column you have eight possible choices, for the second column 7 choices and so on, the number of arrangements is finally 8! respect to the condition above