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 reply to
Solution by Dej Mar)
I now get 48 arrangements within the 5x5, but with 9 of them being situations in which the queen can checkmate the king. In the below array, the bottom-leftmost arrangement allows a queen checkmate. This is the fifth arrangement in the first row of Dej Mar's array, next to another checkmate situation with the queen one position to the left of the top-right corner.
bn... b.n.. .nb.. .nb.. ..bn. ..bn.! ..b.n ..b.n
..r.. ...r. r.... ....r r.... q.... r.... q....
....q ..... ..... ..... ..... ..... ..... .....
..... ....q ...q. ...q. ....q ....r ...q. ...r.
.k... .k... .k... .k... .k... .k.Q. .k... .k...
..b.. .n..b! .n..b ..n.b! ...nb ....b ....b ....b
q.... r.... ..r.. ..... ..r.. q.... ..r.. q....
...r. ..... ..... r.... q.... ....n q.... ...r.
....n ...q. ...q. ...q. ..... ...r. ....n ....n
.k... .k.Q. .k... .k.Q. .k... .k... .k... .k...
...r. ...r. ....q ...q. ...q.! ...r.* ...n.! ...n.
nb... nb... nb... nb... nb... .b... ...b. ...b.
....q ..... ...r. ....r ..... .n... r.... q....
..... ....q ..... ..... ....r ....q ....q ....r
.k... .k... .k... .k... .k.Q. .k... .k.Q. .k...
r....! .....! q.... n.... n.... ...r. ....r ....q
.n.b. .n.b. ...b. ...r. ...q. n.... n.... n....
..... r.... ...n. b.... b.... b.... b.... b....
....q ....q ....r ....q ....r ....q ...q. ...r.
.k.Q. .k.Q. .k... .k... .k... .k... .k... .k...
...q. ...r. ....q ...r. .....! ..... q.... ...r.
n.... ..... ..r.. ..... r.... q.... ..r.. q....
b.... bn... bn... .nb.. .nbQ. ..bn. ...nb ....b
....r ....q ..... ....q ....q ....r ..... ....n
.k... .k... .k... .k... .k... .k... .k... .k...
...q.! q.... ...n. ...n. ....r ..r.. ..q.. .....
r.... ..r.. ..r.. ....r ...n. q.... r.... ..r..
.Q..b ....b q.... q.... q.... ..... ..... q....
....n ....n ...b. ...b. ...b. ...bn ...bn ...bn
.k... .k... .k... .k... .k... .k... .k... .k... 48
Again, exclamation marks mark the checkmate possibilites, with a capital Q showing where the queen could go to do so.
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$(ht, wd)
kr = ht: kc = 2
bd$(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 = 1 THEN
bd$(br, bc) = "b"
FOR nr = 1 TO ht - 1
FOR nc = 1 TO wd
IF (nr < kr - 1 OR ABS(nc - kc) > 1) AND ABS(br - nr) <> ABS(bc - nc) THEN
nkDiffR = ABS(kr - nr): nkDiffC = ABS(kc - nc)
nbDiffR = ABS(br - nr): nbDiffC = ABS(bc - nc)
IF (nkDiffR <> 2 OR nkDiffC <> 1) AND (nkDiffR <> 1 OR nkDiffC <> 2) AND (nbDiffR <> 2 OR nbDiffC <> 1) AND (nbDiffR <> 1 OR nbDiffC <> 2) THEN
bd$(nr, nc) = "n"
FOR rr = 1 TO ht - 1
FOR rc = 1 TO wd
IF (rr < kr - 1 OR ABS(rc - kc) > 1) AND ABS(br - rr) <> ABS(bc - rc) THEN
IF rr <> kr AND rc <> kc AND rr <> nr AND rc <> nc AND rr <> br AND rc <> bc THEN
nrDiffR = ABS(rr - nr): nrDiffC = ABS(rc - nc)
IF (nrDiffR <> 2 OR nrDiffC <> 1) AND (nrDiffR <> 1 OR nrDiffC <> 2) THEN
bd$(rr, rc) = "r"
FOR qr = 1 TO ht - 1
FOR qc = 1 TO wd
IF (qr < kr - 1 OR ABS(qc - kc) > 1) THEN
IF qr <> kr AND qr <> rr AND qr <> br AND qr <> nr AND qc <> kc AND qc <> rc AND qc <> bc AND qc <> nc THEN
IF ABS(qr - kr) <> ABS(qc - kc) AND ABS(qr - br) <> ABS(qc - bc) AND ABS(qr - nr) <> ABS(qc - nc) AND ABS(qr - rr) <> ABS(qc - rc) THEN
nqDiffR = ABS(qr - nr): nqDiffC = ABS(qc - nc)
IF (nqDiffR <> 2 OR nqDiffC <> 1) AND (nqDiffR <> 1 OR nqDiffC <> 2) THEN
bd$(qr, qc) = "q"
good2 = checkmate
'IF good2 OR ABS(rc - kc) <> 1 AND ABS(qc - kc) <> 1 AND ABS(bc - kc) <> 1 AND ABS(nc - kc) <> 1 THEN
r0 = (ct \ 8) * 6 + 1
c0 = (ct MOD 8) * 10 + 1
SELECT CASE (ct \ 8) MOD 2
CASE 0
COLOR 14
CASE 1
COLOR 7
END SELECT
FOR r = 1 TO ht
FOR c = 1 TO wd
LOCATE r0 + r, c0 + c
IF bd$(r, c) > "" THEN
PRINT bd$(r, c);
'IF bd$(r, c) = "Q" THEN bd$(r, c) = ""
ELSE
PRINT ".";
END IF
NEXT
IF r = 1 THEN
IF ABS(rc - kc) <> 1 AND ABS(qc - kc) <> 1 AND ABS(bc - kc) <> 1 AND ABS(nc - kc) <> 1 THEN
PRINT "*";
IF good2 THEN PRINT "!";
ELSE
IF good2 THEN PRINT "!";
END IF
END IF
'PRINT
NEXT
'PRINT
ct = ct + 1
'END IF
FOR rw = 1 TO ht
FOR cl = 1 TO wd
IF bd$(rw, cl) = "" THEN
ph$(rw) = ph$(rw) + "."
ELSE
ph$(rw) = ph$(rw) + bd$(rw, cl)
END IF
NEXT
IF rw = 1 THEN
IF ABS(rc - kc) <> 1 AND ABS(qc - kc) <> 1 AND ABS(bc - kc) <> 1 AND ABS(nc - kc) <> 1 THEN
ph$(rw) = ph$(rw) + "*"
ELSE
ph$(rw) = ph$(rw) + " "
END IF
IF good2 THEN
ph$(rw) = ph$(rw) + "< "
ELSE
ph$(rw) = ph$(rw) + " "
END IF
ELSE
ph$(rw) = ph$(rw) + " "
END IF
NEXT
rwCt = rwCt + 1
IF rwCt = 8 THEN
FOR rw = 1 TO ht
' PRINT #2, ph$(rw)
ph$(rw) = ""
NEXT
' PRINT #2, : PRINT #2,
rwCt = 0
END IF
fff = 0
FOR r = 1 TO ht: FOR c = 1 TO wd
IF bd$(r, c) = "Q" THEN
bd$(r, c) = ""
END IF
NEXT: NEXT
ct2 = ct2 + 1
bd$(qr, qc) = ""
END IF
END IF
END IF
END IF
NEXT qc
NEXT qr
bd$(rr, rc) = ""
END IF
END IF
END IF
NEXT rc
NEXT rr
bd$(nr, nc) = ""
END IF
END IF
NEXT nc
NEXT nr
bd$(br, bc) = ""
END IF
NEXT bc
NEXT br
PRINT ct2
IF rwCt > 0 THEN
FOR rw = 1 TO ht
' PRINT #2, ph$(rw)
ph$(rw) = ""
NEXT
' PRINT #2, : PRINT #2,
rwCt = 0
END IF
CLOSE
FUNCTION checkmate
cmate = 0
FOR dr = -1 TO 1
FOR dc = -1 TO 1
IF dr <> 0 OR dc <> 0 THEN
q2r = qr + dr: q2c = qc + dc
DO WHILE q2r > 0 AND q2r <= ht AND q2c > 0 AND q2c <= wd
IF (q2r < kr - 1 OR ABS(q2c - kc) > 1) THEN
IF qAttack(q2r, q2c, kr, kc, 1) THEN
IF q2r <> rr AND q2c <> rc AND ABS(q2r - br) <> ABS(q2c - bc) THEN
nqDiffR = ABS(q2r - nr): nqDiffC = ABS(q2c - nc)
IF (nqDiffR <> 2 OR nqDiffC <> 1) AND (nqDiffR <> 1 OR nqDiffC <> 2) THEN
good = 1
FOR kdr = -1 TO 1
FOR kdc = -1 TO 1
hid = 1
k2r = kr + kdr
k2c = kc + kdc
IF k2r <= ht AND k2r > 0 AND k2c <= wd AND k2c > 0 THEN
IF qAttack(q2r, q2c, k2r, k2c, 0) THEN hid = 0
' again, this doesn't check for a blocked queen, so may get false checkmate
nkDiffR = ABS(k2r - nr): nkDiffC = ABS(k2c - nc)
IF (nkDiffR = 2 AND nkDiffC = 1) OR (nkDiffR = 1 AND nkDiffC = 2) THEN
hid = 0
END IF
IF k2r = rr OR k2c = rc OR ABS(k2c - bc) = ABS(k2r - br) THEN hid = 0
IF hid THEN good = 0: EXIT FOR
END IF
NEXT
IF good = 0 THEN EXIT FOR
NEXT
IF good THEN
bd$(q2r, q2c) = "Q"
cmate = 1
END IF
END IF
END IF
END IF
END IF
q2r = q2r + dr: q2c = q2c + dc
LOOP
END IF
NEXT dc
NEXT dr
checkmate = cmate
END FUNCTION
FUNCTION qAttack (qRow, qCol, kRow, kCol, isQMove)
IF qRow = kRow OR qCol = kCol OR ABS(qRow - kRow) = ABS(qCol - kCol) THEN
qa = 1
ELSE
qAttack = 0: EXIT FUNCTION
END IF
dr = SGN(kRow - qRow): dc = SGN(kCol - qCol)
r = qRow + dr: c = qCol + dc
DO UNTIL r = kRow AND c = kCol
IF bd$(r, c) > "" AND bd$(r, c) <> "k" THEN qAttack = 0: EXIT FUNCTION
IF isQMove THEN
IF ABS(br - r) = ABS(bc - c) THEN qAttack = 0: EXIT FUNCTION
IF rr = r OR rc = c THEN qAttack = 0: EXIT FUNCTION
nRowDiff = ABS(nr - r): nColDiff = ABS(nc - c)
IF nRowDiff = 1 AND nColDiff = 2 OR nRowDiff = 2 AND nColDiff = 1 THEN
qAttack = 0: EXIT FUNCTION
END IF
END IF
r = r + dr: c = c + dc
LOOP
qAttack = qa
END FUNCTION
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Posted by Charlie
on 2007-10-22 00:17:33 |
re: Solution -- my program fixed
