N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

(In reply to Solution & thoughts by Jer)

DEFDBL A-Z
FOR n = 10 TO 999999
 s$ = LTRIM$(STR$(n))
 sum = 0: prod = 1
 FOR i = 1 TO LEN(s$)
  d = VAL(MID$(s$, i, 1))
  sum = sum + d: prod = prod * d
 NEXT
 IF sum * prod = n THEN
   PRINT n, sum; prod
 END IF
NEXT

finds only the same

135           9  15
144           9  16

as Jer.

Posted by Charlie on 2010-06-21 14:22:24