All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Capital City Conclusion (Posted on 2014-03-06)
In the alphametic: ABC+DEF= 495, the letters A to F denotes a different digit in {1,2,3,6,7,8}.

What are :
6 * 8 * 1 * 2 * * and 8 1 * 6 2 * * 1, when each of them denotes the capital city of a country? Each asterisk denotes a letter (whether same or different) that is not included in the alphametic.

 No Solution Yet Submitted by K Sengupta Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 3

DECLARE SUB permute (a\$)
CLS
DEFDBL A-Z

DATA "6*8*1*2**","81*62**1"

a\$ = "123678": h\$ = a\$
DO
a = VAL(MID\$(a\$, 1, 1))
b = VAL(MID\$(a\$, 2, 1))
c = VAL(MID\$(a\$, 3, 1))
d = VAL(MID\$(a\$, 4, 1))
e = VAL(MID\$(a\$, 5, 1))
f = VAL(MID\$(a\$, 6, 1))
abc = 100 * a + 10 * b + c
defv = 100 * d + 10 * e + f
IF abc + defv = 495 THEN
PRINT abc; " "; defv,
RESTORE
FOR wh = 1 TO 2
FOR i = 1 TO LEN(tmplt\$)
c\$ = MID\$(tmplt\$, i, 1)
IF c\$ = "*" THEN
PRINT c\$;
cap\$ = cap\$ + "*"
ELSE
IF a = VAL(c\$) THEN PRINT "a"; : cap\$ = cap\$ + "a"
IF b = VAL(c\$) THEN PRINT "b"; : cap\$ = cap\$ + "b"
IF c = VAL(c\$) THEN PRINT "c"; : cap\$ = cap\$ + "c"
IF d = VAL(c\$) THEN PRINT "d"; : cap\$ = cap\$ + "d"
IF e = VAL(c\$) THEN PRINT "e"; : cap\$ = cap\$ + "e"
IF f = VAL(c\$) THEN PRINT "f"; : cap\$ = cap\$ + "f"
END IF
NEXT
OPEN "natlcaps.txt" FOR INPUT AS #1
DO
LINE INPUT #1, l\$
ix = INSTR(l\$, ",")
IF ix THEN
l\$ = LTRIM\$(RTRIM\$(LEFT\$(l\$, ix - 1)))
good = 0
IF LEN(l\$) = LEN(cap\$) THEN
good = 1
FOR i = 1 TO LEN(cap\$)
IF MID\$(cap\$, i, 1) <> "*" THEN
IF MID\$(cap\$, i, 1) <> LCASE\$(MID\$(l\$, i, 1)) THEN good = 0: EXIT FOR
END IF
NEXT
IF good THEN
PRINT "    "; l\$; "      ";
END IF
END IF
END IF
LOOP UNTIL EOF(1) OR good = 1
CLOSE 1
PRINT "    ";
NEXT
PRINT
END IF

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

finds

`ABC   DEF       substitutions:127   368    e*f*a*b**                       fa*eb**a128   367    e*c*a*b**                       ca*eb**a167   328    b*f*a*e**                       fa*be**a168   327    b*c*a*e**    Bucharest          ca*be**a    Canberra327   168    e*f*d*b**                       fd*eb**d328   167    e*c*d*b**                       cd*eb**d367   128    b*f*d*e**                       fd*be**d368   127    b*c*d*e**                       cd*be**d`

so ABC = 168 and DEF = 327 and the capital cities are

Bucharest and Canberra.

 Posted by Charlie on 2014-03-06 22:35:41

 Search: Search body:
Forums (0)