In this alphametic equation, six and five are respectively positive integers in base 6 and base 5 notation. Each of the small letters in bold represents a different digit, and none of the numbers contains any leading zero.

(six)₆ = (five)₅

What are the respective minimum value and the maximum value of six?

I used the following code

CLS 0
FOR s = 1 TO 5
 FOR i = 0 TO 5
  IF i <> s THEN
   FOR x = 0 TO 5
    IF x <> s AND x <> i THEN
     FOR f = 1 TO 4
      IF f <> s AND f <> i AND f <> x THEN
       FOR v = 0 TO 4
        IF v <> s AND v <> i AND v <> x AND v <> f THEN
         FOR e = 0 TO 4
          IF e <> s AND e <> i AND e <> x AND e <> f AND e <> v THEN
           n1 = x + 6 * i + 36 * s
           n1s$ = STR$(s) + STR$(i) + STR$(x)
           n2 = e + 5 * v + 5 * 5 * i + 5 * 5 * 5 * f
           n2s$ = STR$(f) + STR$(i) + STR$(v) + STR$(e)
           IF n1 = n2 THEN
            PRINT n1s$ + " in base 6 equals " + n2s$ + " in base 5"
           END IF
          END IF
         NEXT e
        END IF
       NEXT v
      END IF
     NEXT f
    END IF
   NEXT x
  END IF
 NEXT i
NEXT s

and got the 2 solutions

523 base 6 = 1240 base 5

534 base 6 = 1302 base 5

so the minimum value of six is 523 and the maximum is 534

Posted by Daniel on 2009-05-23 12:39:26