AZA
  x AZZA
---------
 AZZZZZA

Substitute a single digit for Z. Substitute any digit for each A. The number for Z must be different from the numbers for A. There are no leading zeros. What are the possible solutions?

DEFDBL A-Z
CLS
FOR z = 0 TO 9
  FOR a1 = 1 TO 9
    IF a1 <> 0 THEN
      FOR a2 = 0 TO 9
       IF a2 <> z THEN
       m1 = 100 * a1 + 10 * z + a2
      FOR a3 = 1 TO 9
       IF a3 <> z THEN
      FOR a4 = 0 TO 9
       IF a4 <> z THEN
       m2 = 1000 * a3 + 110 * z + a4
      FOR a5 = 1 TO 9
       IF a5 <> z THEN
      FOR a6 = 0 TO 9
       IF a6 <> z THEN
         p = 1000000 * a5 + 111110 * z + a6
         IF m1 * m2 = p THEN
            PRINT m1: PRINT m2: PRINT p
         END IF
       END IF
      NEXT
       END IF
      NEXT
       END IF
      NEXT
       END IF
      NEXT
       END IF
      NEXT
    END IF
  NEXT
NEXT

finds

723
7223
5222229

and

645
8441
5444445

Posted by Charlie on 2014-01-31 22:00:07