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 AZ
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 20060409 23:53:36 