Solve separately each of these base ten alphametics. None of the numbers (including those covered under functions) corresponding to any of the following alphametics can contain leading zero.

(I) THOMAS+MALTHUS+1766+1834+RR=RRRRRRR, whenever MOST is divisible by 23.

(II) DINAH+SHORE+1916+1994+TT=TTTTT, where:
sod(DEAR)/sod(HEARTS) = 2/3 and, dr(ROSE) = 4

(III) BENNY+BELL+1906+1999+BBB= DR+DE+MENTO, where:
sod(TRY)/sod(BLEND) = 4/9

Note:sod(x) denotes the sum of digits of x and dr(x) denotes the digital root of x.

CLS
FOR t = 1 TO 9
 IF used(t) = 0 THEN
   used(t) = 1
FOR m = 1 TO 9
 IF used(m) = 0 THEN
   used(m) = 1
FOR r = 1 TO 9
 IF used(r) = 0 THEN
   used(r) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
   used(h) = 1
FOR o = 0 TO 9
 IF used(o) = 0 THEN
   used(o) = 1
FOR a = 0 TO 9
 IF used(a) = 0 THEN
   used(a) = 1
FOR s = 0 TO 9
 IF used(s) = 0 THEN
   used(s) = 1

thomas = t * 100000 + h * 10000 + o * 1000 + m * 100 + a * 10 + s
rr = r * 11
rrrrrrr = r * 1111111
malthus = rrrrrrr - rr - 1834 - 1766 - thomas
t$ = LTRIM$(STR$(thomas))
m$ = LTRIM$(STR$(malthus))
IF LEN(m$) = 7 THEN
IF MID$(t$, 1, 1) = MID$(m$, 4, 1) THEN
IF MID$(t$, 2, 1) = MID$(m$, 5, 1) THEN
IF MID$(t$, 4, 1) = MID$(m$, 1, 1) THEN
IF MID$(t$, 5, 1) = MID$(m$, 2, 1) THEN
IF MID$(t$, 6, 1) = MID$(m$, 7, 1) THEN
 IF used(VAL(MID$(m$, 3, 1))) = 0 AND used(VAL(MID$(m$, 6, 1))) = 0 THEN
 IF MID$(m$, 3, 1) <> MID$(m$, 6, 1) THEN
  most = m * 1000 + o * 100 + s * 10 + t
  IF most MOD 23 = 0 THEN
   PRINT thomas; malthus, r
  END IF
 END IF
 END IF
END IF
END IF
END IF
END IF
END IF
END IF

   used(s) = 0
 END IF
NEXT
   used(a) = 0
 END IF
NEXT
   used(o) = 0
 END IF
NEXT
   used(h) = 0
 END IF
NEXT
   used(r) = 0
 END IF
NEXT
   used(m) = 0
 END IF
NEXT
   used(t) = 0
 END IF
NEXT

finds

THOMAS  MALTHUS             R
840135  1378465             2

Posted by Charlie on 2010-07-25 13:14:22