# Detective chess

rgoudie
Posers and Puzzles 15 Jul '04 20:31
1. 15 Jul '04 20:31
The object of this puzzle is to determine the positions of five chess pieces: a King, Queen, Rook, Bishop, and Knight.

To help you do this, you are given clues in the form of a set of target coordinates where the pieces must be placed. You are also given a set of coordinate/number pairs. In each pair, the corrdinate indicates the square on which the following number must be placed. The number indicates how many pieces are attacking that square, or to put it another way, the number of pieces which could move there in one turn.

When the chess pieces are correctly placed, the numbers on the board will match exactly the number of pieces that attack each numbered square. There is only one solution.

For example, with the information given below, both a Queen nor a Rook cannot be placed on square c3 since each of those two pieces would attach square c6 and that square has zero pieces attacking it. Nor can a Queen or a Bishop be placed on square a8 for the same reason. So you've just eliminated two squares that the Queen can be placed on.

Target squares for pieces:

a8
b1
c3
h4
h8

Set of pairs:

(b8, 1)
(c6, 0)
(e5, 1)
(f5, 1)
(f8, 1)

-Ray.
2. 16 Jul '04 08:142 edits
Originally posted by rgoudie
The object of this puzzle is to determine the positions of five chess pieces: a King, Queen, Rook, Bishop, and Knight.

To help you do this, you are given clues in the form of a set of target coordinates where the pieces must be placed. ...[text shortened]... f pairs:

(b8, 1)
(c6, 0)
(e5, 1)
(f5, 1)
(f8, 1)

-Ray.
a8 knight
b1 bishop
c3 king
h4 rook
h8 queen

reasoning: f8 can only be covered by Q or R on h8 (Q on a8 not possible for c6 and R on a8 leaves only Queen on h4 but then e5 and f5 can't be covered at the same time anymore). But if R on h8, then Q can only be on h4 to avoid violation on b8 or c6. But then there are no two pieces left to cover both e5 and f5. Hence: Q on h8.

Rook can only go on h4, otherwise we have a violation on b8 or c6.

Bishop is the only remaining piece left to cover f5 from b1.

King on c3 because on a8 we have violation on b8.

Knight on only place left doing nothing.
3. 16 Jul '04 13:55
Originally posted by Mephisto2
a8 knight
b1 bishop
c3 king
h4 rook
h8 queen
Obviously correct.

-Ray.