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Repeating decimals (Posted on 2006-09-25) Difficulty: 3 of 5
The decimal expansion of 1/271 repeats with a period of length 5:
.003690036900369 ...

However, it is not the smallest number q for which the decimal expansion of 1/q has a repetition length of 5.

Find the smallest q so that the decimal expansion of 1/q has repetition length n for each of {1, 2, ..., 10}

Is there a simple way of finding such a number?

See The Solution Submitted by Jer    
Rating: 4.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Thoughts K Sengupta2023-02-22 07:53:14
re(6): General solutionRichard2006-09-27 15:52:05
re(5): General solutionOld Original Oskar!2006-09-27 11:47:07
re(4): General solutionRichard2006-09-26 23:07:48
Some Thoughtsre(3): General solutionOld Original Oskar!2006-09-26 16:14:41
Some Thoughtsre(2): General solutionFederico Kereki2006-09-26 11:34:15
re: General solutionJer2006-09-26 11:17:03
SolutionGeneral solutionFederico Kereki2006-09-26 10:58:27
re(3): computer explorationbrianjn2006-09-25 23:36:50
re(2): computer explorationJer2006-09-25 11:46:38
Hints/Tipsre: computer explorationCharlie2006-09-25 11:35:02
Hints/Tipscomputer explorationCharlie2006-09-25 11:03:49
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