Each of the letters should be replaced by a different digit from 1 to 9 to satisfy this alphanumeric equation:

 A     C     E
--- + --- + --- = 1, with A > C > E
 B     D     F

Can you solve it, knowing that if I told you whether CA is a prime number or not, you would be able to tell me all the other letters?

Note: CA denotes the concatenation of the digits.

DEFDBL A-Z
FOR e = 1 TO 7
  used(e) = 1
FOR c = e + 1 TO 8
  used(c) = 1
FOR a = c + 1 TO 9
  used(a) = 1

  FOR b = 1 TO 9
    IF used(b) = 0 THEN
       used(b) = 1
  FOR d = 1 TO 9
    IF used(d) = 0 THEN
       used(d) = 1
  FOR f = 1 TO 9
    IF used(f) = 0 THEN
       used(f) = 1

       IF a * d * f + c * b * f + e * b * d = b * d * f THEN
          PRINT STR$(a); "/"; LTRIM$(STR$(b)); " +";
          PRINT STR$(c); "/"; LTRIM$(STR$(d)); " +";
          PRINT STR$(e); "/"; LTRIM$(STR$(f))
       END IF

       used(f) = 0
    END IF
  NEXT
       used(d) = 0
    END IF
  NEXT
       used(b) = 0
    END IF
  NEXT

  used(a) = 0
NEXT
  used(c) = 0
NEXT
  used(e) = 0
NEXT

finds

 3/6 + 2/8 + 1/4
 3/9 + 2/4 + 1/6
 4/8 + 3/9 + 1/6
 
CA = 23 in both of the first two, but 34 in the third. Only if told that it was not prime would we be able to determine the letters. So the letters, in alphabetic order, represent 4, 8, 3, 9, 1 and 6.

Posted by Charlie on 2012-10-01 13:51:26