X is a positive eight-digit base ten integer of the form CONSIDER where each of the capital letters in bold denotes a different base ten digit from 0 to 9, and satisfies all of the following conditions, where C is nonzero.

• CO is divisible by 2.
• CON is divisible by 3.
• CONS is divisible by 4.
• CONSI is divisible by 5.
• CONSID is divisible by 6.
• CONSIDE is divisible by 7.
• CONSIDER is divisible by 8.

Determine the respective minimum and maximum value of X.

The possible values of x:

12965408
30925864
36925840
38165472
72965480
78320416
78920456
80165472
92765408

DECLARE SUB addOn ()
DEFDBL A-Z
DIM SHARED used(9), st$, ct
FOR i = 1 TO 9
 used(i) = 1
 st$ = LTRIM$(STR$(i))
 addOn
 used(i) = 0
NEXT
PRINT ct
END

SUB addOn
 FOR i = 0 TO 9
  IF used(i) = 0 THEN
    used(i) = 1
    st$ = st$ + LTRIM$(STR$(i))
    v = VAL(st$)
    IF v MOD LEN(st$) = 0 THEN
      IF LEN(st$) = 8 THEN
        PRINT st$: ct = ct + 1
      ELSE
        addOn
      END IF
    END IF
    st$ = LEFT$(st$, LEN(st$) - 1)
    used(i) = 0
  END IF
 NEXT
END SUB

 

Posted by Charlie on 2009-11-05 16:58:13