While still at home the Black King,
in rather similar circumstances as his White oppressor, finds disarray at Court [K, Q, QB, QKt, QR] on his Queen’s side.
Again, he is the only occupant of the first rank and all 5 pieces are spread within the domain [K1 – QR5] with none being a direct threat to another.
Find a situation where the occupants again enjoy a lesser domain, and the Queen again can force ‘mate’ without herself being under any threat; after a successful "coup d'etat" who cares if another is also under threat?
Bonus:
I offer 28 scenarios where the Court enjoys 'serenity', but how many fit the "more reduced" domain category?.
My program for the white court required little change from its final debugged state. The king is now in the leftmost file of the 5x5 section and the bishop is on the same color square as the king. The new version's first few lines contain the changes:
DECLARE FUNCTION qAttack! (qRow!, qCol!, kRow!, kCol!, isQMove!)
DECLARE FUNCTION checkmate! ()
DIM SHARED br, bc, nr, nc, rr, rc, kr, kc, qr, qc, ht, wd
ht = 5: wd = 5
CLS
'oPEN "anarchy2.txt" FOR APPEND AS #2
REDIM SHARED bd$(ht, wd)
kr = ht: kc = 1
bd$(ht, kc) = "k"
FOR br = 1 TO ht - 1
FOR bc = 1 TO wd
IF (br < kr - 1 OR ABS(bc - kc) > 1) AND ABS(br - kr) <> ABS(bc - kc) AND (ABS(br - kr) + ABS(bc - kc)) MOD 2 = 0 THEN
bd$(br, bc) = "b"
...
The rest of the program is the same.
The program again finds 48 non-attacking arrangements:
bn... bn... bn... b.n..* b..n. b...n b...n* b....
..r.. ..... ..... ...r. ..... ...r. ...r. n....
....q ....r ....q ..... .r... .q... ..... .r...
..... ..q.. ..r.. ....q ....q ..... ..q.. ....q
k.... k.... k.... k.... k.... k.... k.... k....
b....* b....* n.b..* .nb.. .nb.. ..bn. ..b.n ..b.n
n.... ...r. ....q ....r ....q ..... ..... .....
....q n.... ..... ..... ..... .r... .r... .q...
..r.. ....q ...r. ...q. ...r. ....q ...q. ...r.
k.... k.... k.... k.... k.... k.... k.... k....
.n... .n... ...r. ...r. ....r ...q. ...q. .....
.b... .b... nb... nb... nb... nb... nb... nb...
....r ....q ....q ..... ...q. ....r ..... ....q
..q.. ..r.. ..... ....q ..... ..... ..r.. ..r..
k.... k.... k.... k.... k.... k.... k.... k....
...q.! n....* n....* n....* ....n* .r... ...r.* ....r*
nb... ...r. ...r. ....q ...r. n.... n.... n....
..... b.... b.... b.... b.... b.... b.... b....
....r ..q.. ....q ...r. ..q.. ...q. ....q ...q.
k..Q. k.... k.... k.... k.... k.... k.... k....
...q.* ...q.* .q... .q... .q... n.... ....n ....n
n.... n.... ....n ...r. ..... .r... .r... .q...
b.... b.... b.... b...n b...n ....b ....b ....b
..r.. ....r ..r.. ..... ...r. ..q.. ..q.. ..r..
k.... k.... k.... k.... k.... k.... k.... k....
...q.* .q... ...q. ...r. ...q. ..r..* ..r.. ..q..
n.... ....n .r... .q... .r... ....q ..... .....
....b ....b n...b ....b ....b n.... .q... .r...
..r.. ..r.. ..... ....n ....n ...b. ...bn ...bn
k.... k.... k.... k.... k.... k.... k.... k.... 48
The above shows only one non-attacking arrangement where the queen has a possible checkmate move (bold solution), and that uses the full 5x5 section of the board. The only arrangement that doesn't use the full 5x5, the last one in the third row, does not allow the queen a checkmate move, as the bishop guards the lower right corner and the rook guards the center of the kings row(rank).
If a redefinition of "reduced" is allowed--4 high by 6 wide for an area of only 24 instead of 25-- then this solution is possible:
n.b...!
.....r
...q..
.k.Q..
Again capital Q marks where the queen should go to checkmate the king in the solution marked with exclamation (!).
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Posted by Charlie
on 2007-10-25 11:23:17 |
Computer program solution
