How many ways are there to put two black rooks on a 8x8 chessboard so that they don't attack each other? There are several ways that these two could be placed, and I am wondering how many amount of positions there are. Thank you for any contribution.


marked as duplicate by Xander Henderson, mlc, Donald Splutterwit, José Carlos Santos, Leucippus Oct 10 '17 at 0:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Again, too many rooks being placed. The end result though is that you need to simultaneously select two rows and two columns. You then pick which row was paired with which column. $\endgroup$ – JMoravitz Oct 9 '17 at 19:31
  • $\begingroup$ Whether you have 8 rooks or only two the same basic rules apply. Consider basic solutions, then use symmetries of the board to generalize. $\endgroup$ – Xander Henderson Oct 9 '17 at 19:31
  • $\begingroup$ math.stackexchange.com/questions/2283548/… $\endgroup$ – Xander Henderson Oct 9 '17 at 19:31
  • 1
    $\begingroup$ The first rook can be placed in $64$ ways, the second rook can be placed in $49$ ways, each configuration can be attained in $2$ ways ... $ 32 \times 49$. $\endgroup$ – Donald Splutterwit Oct 9 '17 at 19:32

Hint: If you place one rook how many squares are now not available to the second rook, because placing it there would attack the first rook?


Not the answer you're looking for? Browse other questions tagged or ask your own question.