Repeating decimals (Posted on 2006-09-25)

	Submitted by Jer
Rating: 4.5000 (2 votes)
Solution:	(Hide)
1/3 = .333... 1/11 = .090909... 1/27 = .037037037... 1/101 = .009900990099... 1/41 = .024390243902439... 1/7 = .142857142857142857... 1/239 = .004184100418410041841... 1/73 = 013698630136986301369863... 1/81 = .012345679012345679012345679... 1/451 = .02217294900221729490022172949... If you factor 10^n-1 as Charlie did, http://perplexus.info/show.php?pid=5062&cid=34345 it is apparent the smallest q is a factor of this number. The rule is that q should be the smallest factor that is not a factor of one of the previous rep-9's. For example rep length 12 factors as 3*3*3*7*11*13*37*101*9901. Each of these individual factors occurs in a previous row of the chart, as do many combinations of them (such as 3*3*3*7 which would have rep length 6). The smallest comibination that does not occur higher in the chart is 7*101 which is why 707 is the smallest q with rep length 12. See http://mathworld.wolfram.com/DecimalExpansion.html for more about finding such numbers.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-02-22 07:53:14
	re(6): General solution	Richard	2006-09-27 15:52:05
	re(5): General solution	Old Original Oskar!	2006-09-27 11:47:07
	re(4): General solution	Richard	2006-09-26 23:07:48
	re(3): General solution	Old Original Oskar!	2006-09-26 16:14:41
	re(2): General solution	Federico Kereki	2006-09-26 11:34:15
	re: General solution	Jer	2006-09-26 11:17:03
	General solution	Federico Kereki	2006-09-26 10:58:27
	re(3): computer exploration	brianjn	2006-09-25 23:36:50
	re(2): computer exploration	Jer	2006-09-25 11:46:38
	re: computer exploration	Charlie	2006-09-25 11:35:02
	computer exploration	Charlie	2006-09-25 11:03:49