Turmoil reigns at the Court of the White King; all pieces oppose one another.

The King and his entourage (The queen, king, and the 3 pieces to his right) can be spread inside the 5 x 5 domain from [Q1 - KR5] with only the King on the first rank, where he is at home.

During this state of upheaval no piece threatens another.

Within a smaller domain than the given 5x5 space, place the pieces such that the Queen can force "mate" in just one move while remaining free from aggression herself, though possibly threatening others. (I note two different arrangements)

Note:
1. Other than the "domestic aggression" all chess rules still apply.
2. No dimension of the smaller domain is greater than 5.

Bonus:
1. How many cases of the White Court's disarray can you find? I have slightly over 30.

2. Offer one where Q and KB files are vacant.

In the anarchial courtyard of the White King, there are nine scenarios that the Queen can "mate" the King in one move.
Of the nine, the two scenarios of smaller courtyards are:

+---+---+---+---+---+   +---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |
+---+---+---+---+---+   +---+---+---+---+---+
| R |   |   |   |   |   |   | N |   | B |   |
+---+---+---+---+---+   +---+---+---+---+---+
|   | N | B | * |   |   | R |   |   |   |   |
+---+---+---+---+---+   +---+---+---+---+---+
|   |   |   |   | Q |   |   |   |   |   | Q |
+---+---+---+---+---+   +---+---+---+---+---+
|   | K |   |   |   |   |   | K |   | * | * |
+---+---+---+---+---+   +---+---+---+---+---+
The position the Queen can force "mate" is indicated by an asterisk [*].

(Bonus)
1. There are 48 different scenarios for the arrangement of the White Court where none personally attacks each other. (A total of 9 scenarios with small [4x5 or 5x4] courtyards).
2. The small courtyard with the vacant Q and KB files is:

+---+---+---+---+---+ 
|   |   |   | R |   | 
+---+---+---+---+---+ 
|   | B |   |   |   | 
+---+---+---+---+---+ 
|   | N |   |   |   | 
+---+---+---+---+---+ 
|   |   |   |   | Q | 
+---+---+---+---+---+ 
|   | K |   |   |   | 
+---+---+---+---+---+ 

The 48 courtyard arrangements:

Q....  Q....  Q....  ..Q..  ...Q.  ...Q.  
..R..  ...B.  ..R..  R....  R....  NB...  
...NB  ...N.  ....B  .....  .!..B  .....  
.....  ....R  ....N  ...BN  ....N  ....R  
.K...  .K...  .K...  .K...  .K...  .K.!.  

...Q.  ...Q.  ....Q  ....Q  ....Q  ..R..  
NB...  N....  ..R..  NB...  N....  Q....  
....R  B....  BN...  ...R.  B....  .....  
.....  ....R  .....  .....  ...R.  ...BN    
.K...  .K...  .K...  .K...  .K...  .K...  

...R.  ..B.N  ..B..  ..BN.  ....B  .....
Q....  Q....  Q....  Q....  Q....  Q....
....B  .....  ...R.  .....  ....N  ..BN.
....N  ...R.  ....N  ....R  ...R.  ....R
.K...  .K...  .K...  .K.!.  .K...  .K...

N....  ...N.  ....R  ...N.  ...NB  ...NB
...Q.  ..R..  ...N.  ...B.  ..R..  ..R..
B....  Q....  Q....  Q....  Q....  Q....
....R  ...B.  ...B.  ....R  .....  .....
.K...  .K...  .K...  .K...  .K...  .K...

.....  ....B  BN...  ...R.  .NB..  ..B.N
..R..  ..R..  ..R..  NB...  R....  .....
Q....  Q....  ....Q  ....Q  .....  R....
...BN  ....N  .....  .....  ...Q.  ...Q.
.K...  .K...  .K...  .K...  .K...  .K...

.N..B  ....R  .N..B  ..N.B  .NB..  ..B.N
..R..  N....  R....  .....  ....R  R....
.....  B....  .....  R....  .....  .....
...Q.  ...Q.  ...Q.  ...Q.  ...Q.  ...Q.
.K...  .K...  .K.!.  .K.!.  .K...  .K...

R....  ...N.  ...R.  ...R.  .....  N....
.N.B.  ...B.  NB...  .B...  R....  ...R.
.....  R....  .....  .N...  .NB!.  B....
....Q  ....Q  ....Q  ....Q  ....Q  ....Q
.K.!!  .K.!.  .K...  .K...  .K...  .K...

...R.  .....  ...R.  ...R.  ..BN.  B.N..
.....  .N.B.  N....  .....  R....  ...R.
.NB..  R....  B....  BN...  .....  .....
....Q  ....Q  ....Q  ....Q  ....Q  ....Q
.K...  .K.!!  .K...  .K...  .K...  .K...

 

Edited on October 22, 2007, 9:00 am

Posted by Dej Mar on 2007-10-19 15:30:35