perplexus.info :: Numbers : 3's & 7's

3's & 7's (Posted on 2006-04-09)

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.

Submitted by Jer

Rating: 3.2500 (4 votes)

Solution: (Hide)

Rules 2 and 4 are equivalent. We need the number of 7's to be a multiple of three and the number 3's to be a multiple of 7 to satisfy rules 1, 2, 3, 5 and 6.
3333333777 is the smallest such number but does not fit rule 4.
Rearranging the digits a bit gives the smallest that does as 3333377733

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: official solution	Ady TZIDON	2014-11-20 22:40:59
Puzzle Solution	K Sengupta	2008-07-08 15:55:28
answer	K Sengupta	2008-07-07 15:28:34
re(2): the computer doing the trial and error	stewart	2006-04-10 07:43:56
re: the computer doing the trial and error	stewart	2006-04-10 07:23:03
the computer doing the trial and error	Charlie	2006-04-09 23:53:36
My solution	cordell	2006-04-09 22:48:22
One solution	Pat Scanlan	2006-04-09 22:15:30
Solution.	Dej Mar	2006-04-09 20:57:23
re: answer??	Andrew	2006-04-09 20:47:36
answer??	Andrew	2006-04-09 20:44:46
re: Solution (with some trial and error)	Tristan	2006-04-09 20:28:21
Solution (with some trial and error)	Leming	2006-04-09 18:22:45

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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info