Find a four-digit number with four different digits, that is equal to the number formed by its digits in descending order minus the number formed by its digits in ascending order.

(In reply to My solution by Gamer)

Proof of uniqueness of the solution is obtained by the following program that looks at all numbers formed with four different digits in ascending sequence and subtracting that from it's reverse and sees if the result has the same four digits. It includes the possibility that the leading digit is zero. Only 7641 - 1467 = 6174 is found by the program.

FOR i = 0 TO 6
  FOR j = i + 1 TO 7
    FOR k = j + 1 TO 8
      FOR l = k + 1 TO 9
        diff = l * 1000 + k * 100 + j * 10 + i - (i * 1000 + j * 100 + k * 10 + l)
        s$ = LTRIM$(STR$(diff))
        IF LEN(s$) < 4 THEN
          s$ = RIGHT$("0000" + s$, 4)
        END IF
        s1$ = LTRIM$(STR$(l * 1000 + k * 100 + j * 10 + i))
        DO
         ix = INSTR(s1$, LEFT$(s$, 1))
         IF ix = 0 THEN EXIT DO
         s1$ = LEFT$(s1$, ix - 1) + MID$(s1$, ix + 1)
         s$ = MID$(s$, 2)
        LOOP UNTIL s$ = ""
        IF s$ = "" THEN
          d = l * 1000 + k * 100 + j * 10 + i
          a = i * 1000 + j * 100 + k * 10 + l
          PRINT d; "-"; a; "="; d - a
        END IF
      NEXT
    NEXT
  NEXT
NEXT

Posted by Charlie on 2003-04-26 09:17:17