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.

DECLARE FUNCTION dr# (x#)
DECLARE FUNCTION sod# (x#)
DEFDBL A-Z
FOR d = 1 TO 9
 IF used(d) = 0 THEN
   used(d) = 1
FOR s = 1 TO 9
 IF used(s) = 0 THEN
   used(s) = 1
FOR t = 1 TO 9
 IF used(t) = 0 THEN
   used(t) = 1
FOR i = 0 TO 9
 IF used(i) = 0 THEN
   used(i) = 1
FOR n = 0 TO 9
 IF used(n) = 0 THEN
   used(n) = 1
FOR a = 0 TO 9
 IF used(a) = 0 THEN
   used(a) = 1
FOR h = 0 TO 9
 IF used(h) = 0 THEN
   used(h) = 1

tt = t * 11
ttttt = t * 11111
dinah = d * 10000 + i * 1000 + n * 100 + a * 10 + h
shore = ttttt - tt - 1994 - 1916 - dinah

d$ = LTRIM$(STR$(dinah))

s$ = LTRIM$(STR$(shore))
IF LEN(s$) = 5 THEN
 IF MID$(d$, 5, 1) = MID$(s$, 2, 1) AND VAL(MID$(s$, 1, 1)) = s THEN
  o = VAL(MID$(s$, 3, 1))
  r = VAL(MID$(s$, 4, 1))
  e = VAL(MID$(s$, 5, 1))
  IF used(o) = 0 AND used(r) = 0 AND used(e) = 0 THEN
   dear = d * 1000 + e * 100 + a * 10 + r
   hearts = h * 100000 + e * 10000 + a * 1000 + r * 100 + t * 10 + s
   rose = r * 1000 + o * 100 + s * 10 + e
   IF 3 * sod(dear) = 2 * sod(hearts) AND dr(rose) = 4 THEN
      PRINT dinah; shore, t
   END IF
  END IF
 END IF
END IF

   used(h) = 0
 END IF
NEXT
   used(a) = 0
 END IF
NEXT
   used(n) = 0
 END IF
NEXT
   used(i) = 0
 END IF
NEXT
   used(t) = 0
 END IF
NEXT
   used(s) = 0
 END IF
NEXT
   used(d) = 0
 END IF
NEXT

FUNCTION dr (x)
  v = x
  DO
    v = sod(v)
  LOOP UNTIL v < 10
  dr = v
END FUNCTION

FUNCTION sod (x)
 xs$ = LTRIM$(STR$(x))
 t = 0
 FOR i = 1 TO LEN(xs$)
   t = t + VAL(MID$(xs$, i, 1))
 NEXT
 sod = t
END FUNCTION

finds

DINAH  SHORE                T
16903  23587                4

Posted by Charlie on 2010-07-25 13:54:53