Viktor got very famous in Hogwarts after he broke all records in the tile game. Even Hermoine was impressed. Ron out of envy, decided to challenge Viktor with one of his chess puzzles. If Viktor could not solve the puzzle, Viktor can not ask Hermoine out to the ball. Viktor needs all the help he can to solve the puzzle, so help him out. The puzzle is described as follows: On a `3 xx 3` chess board, 4 knights, 3 rooks and 2 bishops (of the same color) must be arranged in such a way that each piece must be protected:
1. in the final arrangement.
2. in the positions where either of the 4 knights/3 rooks/2 bishops are placed in their final place. Let the pieces be assigned numbers as follows: Knight=2, Bishop=3, Rook=5 on black squares and respective negative values on white squares. Find out the “sum” of all pieces in the arranged position. (Assume there are 5 black squares on the chess board).
A. 1
B. 6
C. 9
D. 13
