Find the smallest number comprised of only 3’s and 7’s which fits the following conditions:

1) It has at least one 3;
2) It has at least one 7;
3) It is divisible by 3;
4) It is divisible by 7;
5) The sum of its digits is divisible by 3;
6) The sum of its digits is divisible by 7.

DEFDBL A-Z
DECLARE SUB permute (a$)
CLS
a$ = "3333333777": h$ = a$
DO
  n = VAL(a$)
  q = INT(n / 7)
  r = n - q * 7
  IF r = 0 THEN PRINT a$
  permute a$
LOOP UNTIL a$ = h$

yields the 16 smallest such numbers:

3333377733
3333737337
3333773373
3337333377
3337737333
3373337373
3373773333
3377333337
3733333737
3733377333
3737333733
7333373733
7333733337
7337733333
7373333373
7733373333

Posted by Charlie on 2006-04-09 23:53:36