+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    |    |    |    |    |    |    |    |
+----+----+----+----+----+----+----+----+
|    | 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.)

For ease I'm ignoring chess notation for locations.

The King threatens all 8 adjacent squares surrounding it.
To the right of the King place the 4 Bishops in the same row.  Then after the farthest right bishop place a Queen.  On the lowest row and in the 5th column from the left place the second Queen.

Now, all unoccupied squares are threatened.

There is something however in the text that implies that this is not the correct solution.  Some of the occupied squares are threatened but not all.  It seems to me that one would have to relocate pieces and identify pieces such that even the occupied squares are threatened.

Posted by brianjn on 2013-05-09 23:35:34