All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
3's & 7's (Posted on 2006-04-09) Difficulty: 3 of 5
Find the smallest number comprised of only 3ís and 7ís 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.

See The Solution Submitted by Jer    
Rating: 3.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution. | Comment 5 of 13 |

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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information