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3's & 7's (Posted on 2006-04-09) Difficulty: 3 of 5
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
Some Thoughtsre: official solutionAdy TZIDON2014-11-20 22:40:59
SolutionPuzzle SolutionK Sengupta2008-07-08 15:55:28
answerK Sengupta2008-07-07 15:28:34
re(2): the computer doing the trial and errorstewart2006-04-10 07:43:56
re: the computer doing the trial and errorstewart2006-04-10 07:23:03
Solutionthe computer doing the trial and errorCharlie2006-04-09 23:53:36
My solutioncordell2006-04-09 22:48:22
One solutionPat Scanlan2006-04-09 22:15:30
SolutionSolution.Dej Mar2006-04-09 20:57:23
re: answer??Andrew2006-04-09 20:47:36
answer??Andrew2006-04-09 20:44:46
re: Solution (with some trial and error)Tristan2006-04-09 20:28:21
SolutionSolution (with some trial and error)Leming2006-04-09 18:22:45
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