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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.)
re: Solution (with some trial and error) | Comment 2 of 13 |
(In reply to Solution (with some trial and error) by Leming)

If you wanted to eliminate some of the trial and error, you could calculate 3*10^n mod 7
3*10^n  = {3,2,6,4,5,1,3,2,6,4...}mod 7 (starting with n=0)
The sum of all those is 1 mod 7
Therefore you have to eliminate three of the elements the sum of which must be 1 mod 7.

  Posted by Tristan on 2006-04-09 20:28:21

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