+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    | WK |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+

Place 2 queens, 2 white bishops and 2 black bishops on this chessboard so that every square is under attack.

One white king has already been placed (as shown in the above diagram.)

(In reply to One Solution by Salil)

Now that is very pleasing.

It does answer for me, "should the occupied square also be under attack?"  Clearly no.

I had been thinking that Qs have 4 lines of attack and Bs just 2.  At most the Qs and Bs can cover up to 6 diagonals.

This solution however does provide another benefit!  I can give up trying to bust my brain for a computer solution, although in doing so I've learnt a few new programming tricks. 

Manny thanks KS for the problem and Salil for this solution.

Posted by brianjn on 2013-05-13 05:05:31