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.

I solved this before looking at Leming's solution.  As is this, his is a correct solution, arrived at similar means.

3333377733 is the smallest number comprised of solely of 3s and 7s. 

1) 3333377733 has at least one 3.
2) 3333377733 has at least one 7. 
3) 3333377733 / 3 = 1111125911, thus it is divisble by 3.
4) 3333377733 / 7 = 476196819, thus it is divisible by 7.

3+3+3+3+3+7+7+7+3+3 = 42

5) 42 / 3 = 14, thus the sum of its digits is divisible by 3. 
6) 42 / 7 = 6, thus the sum of its digits is divisible by 7.

Edited on April 9, 2006, 9:02 pm

Posted by Dej Mar on 2006-04-09 20:57:23