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 Nine cards (Posted on 2005-10-14)
Nine cards are disposed as shown:
```           +---+---+---+
| a | b | c |
+---+---+---+
| d | e | f |
+---+---+---+
| g | h | i |
+---+---+---+
```

1) There are, at least, two Aces, two Kings, two Queens and two Jacks.
2) Every Ace borders a King and a Queen.
3) Every King borders a Queen and a Jack.
4) Every Queen borders a Jack.
Note: "border" means "touch" horizontally or vertically, not diagonally.

Identify the nine cards.

 See The Solution Submitted by pcbouhid Rating: 2.7500 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer logic | Comment 8 of 30 |
(In reply to re(2): solution by derek)

The computer program below tries all permutations of "aakkqqjj?", where the ? stands for any one card. an array is used to indicate the positions which are considered adjacent to a particular position, with the 0 element of each row representing how many adjacencies are within that row. (The row represents the position whose adjacencies are needed.)

The same four rotated versions were found as found by derek, but each was repeated 3 times, as any of the three queens could be the one represented by the ?.  When a hit is found, the logic is gone through again to assure that the substitution of a specific character for the ? did not create new needs (the Q requiring an adjacent J, whereas a ? did not require anything in particular).

DECLARE SUB permute (a\$)
CLS
a\$ = "aakkqqjj?": h\$ = a\$

cnct(1, 0) = 2: cnct(1, 1) = 2: cnct(1, 2) = 4
cnct(3, 0) = 2: cnct(3, 1) = 2: cnct(3, 2) = 6
cnct(7, 0) = 2: cnct(7, 1) = 8: cnct(7, 2) = 4
cnct(9, 0) = 2: cnct(9, 1) = 6: cnct(9, 2) = 8
cnct(2, 0) = 3: cnct(2, 1) = 1: cnct(2, 2) = 5: cnct(2, 3) = 3
cnct(4, 0) = 3: cnct(4, 1) = 1: cnct(4, 2) = 5: cnct(4, 3) = 7
cnct(6, 0) = 3: cnct(6, 1) = 9: cnct(6, 2) = 5: cnct(6, 3) = 3
cnct(8, 0) = 3: cnct(8, 1) = 9: cnct(8, 2) = 5: cnct(8, 3) = 7
cnct(5, 0) = 4: cnct(5, 1) = 2: cnct(5, 2) = 4: cnct(5, 3) = 6: cnct(5, 4) = 8

DO
good = 1
a2\$ = a\$
FOR p = 1 TO 9
b\$ = ""
SELECT CASE MID\$(a2\$, p, 1)
CASE "a"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "k") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "k"
ELSE
good = 0: EXIT FOR
END IF
END IF
IF INSTR(b\$, "q") = 0 THEN
IF INSTR(b\$, "?") > 0 AND INSTR(a2\$, "?") > 0 THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "q"
ELSE
good = 0: EXIT FOR
END IF
END IF
CASE "k"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "j") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "j"
ELSE
good = 0: EXIT FOR
END IF
END IF
IF INSTR(b\$, "q") = 0 THEN
IF INSTR(b\$, "?") > 0 AND INSTR(a2\$, "?") > 0 THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "q"
ELSE
good = 0: EXIT FOR
END IF
END IF
CASE "q"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "j") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "j"
ELSE
good = 0: EXIT FOR
END IF
END IF
END SELECT
NEXT p
IF good THEN

FOR p = 1 TO 9
b\$ = ""
SELECT CASE MID\$(a2\$, p, 1)
CASE "a"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "k") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "k"
ELSE
good = 0: EXIT FOR
END IF
END IF
IF INSTR(b\$, "q") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "q"
ELSE
good = 0: EXIT FOR
END IF
END IF
CASE "k"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "j") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "j"
ELSE
good = 0: EXIT FOR
END IF
END IF
IF INSTR(b\$, "q") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "q"
ELSE
good = 0: EXIT FOR
END IF
END IF
CASE "q"
FOR i = 1 TO cnct(p, 0)
b\$ = b\$ + MID\$(a2\$, cnct(p, i), 1)
NEXT
IF INSTR(b\$, "j") = 0 THEN
IF INSTR(b\$, "?") THEN
ix = INSTR(a2\$, "?")
MID\$(a2\$, ix, 1) = "j"
ELSE
good = 0: EXIT FOR
END IF
END IF
END SELECT
NEXT p

IF good THEN
rw1 = (ct \ 4) * 5 + 1
cl1 = (ct MOD 4) * 10 + 1

ct = ct + 1

LOCATE rw1, cl1: PRINT LEFT\$(a2\$, 3);
LOCATE rw1 + 1, cl1: PRINT MID\$(a2\$, 4, 3)
LOCATE rw1 + 2, cl1: PRINT RIGHT\$(a2\$, 3)
LOCATE rw1 + 3, cl1: PRINT a\$
PRINT
END IF

END IF
permute a\$
LOOP UNTIL a\$ = h\$

 Posted by Charlie on 2005-10-14 15:25:20

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