Ever wonder why women talk so much? It all started with Eve, and not only did she talk, but she kept on talking forever (if only through the generations of women to come).

The following equation, in which each letter represents a different digit, shows this phenomenon as an infinitely repeating decimal:

EVE/DID=.TALKTALKTALKTALK...

What number does each letter represent?

(In reply to Solution (no computer program used) by Charlie)

212 / 606 = .34983498...
242 / 303 = .79867986...

are both solutions, found by:

CLS
DEFDBL A-Z
FOR e = 1 TO 9
 FOR v = 0 TO 9
  IF v <> e THEN
  FOR d = 1 TO 9
   IF d <> e AND d <> v THEN
   FOR i = 0 TO 9
    IF i <> d AND i <> e AND i <> v THEN
     did = 101 * d + i * 10
     eve = 101 * e + v * 10
     talk = 9999 * eve / did
     IF talk = INT(talk) AND talk > 1000 AND talk < 9999 THEN
       t$ = LTRIM$(STR$(e)) + LTRIM$(STR$(v)) + LTRIM$(STR$(d)) + LTRIM$(STR$(i))
       good = 1
       talk$ = LTRIM$(STR$(talk))
       FOR j = 1 TO 4
        IF INSTR(t$, MID$(talk$, j, 1)) > 0 THEN good = 0: EXIT FOR
        t$ = t$ + MID$(talk$, j, 1)
       NEXT
       IF good THEN
        PRINT eve, did, talk
       END IF
     END IF
    END IF
   NEXT
   END IF
  NEXT
  END IF
 NEXT
NEXT

Posted by Charlie on 2003-12-10 11:29:39