tag:blogger.com,1999:blog-5871184605628305545.post8529906679354416757..comments2013-05-25T03:36:33.414-07:00Comments on Puzzled: Four Digit Whole NumberAnonymoushttp://www.blogger.com/profile/02364548875097103884noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5871184605628305545.post-66823395152172007412012-08-14T01:51:54.282-07:002012-08-14T01:51:54.282-07:00Clearly the last digit should be 0 or 1 or 5 or 6....Clearly the last digit should be 0 or 1 or 5 or 6. It can't be 0 because that would lead to the number being 0000.<br /><br />Notice that n^2 - n = n(n-1) is divisible by 10000 = 16*625.<br /><br />If n ends in 1, n-1 ends in 0 which means 10000 divides n-1 which is not possible since n is four digit. So, this is not the case.<br /><br />If n ends in 5, n = 625m and n= 16k+1 . Since 625%16 = 1, the least possible value of n > 625 is 625*17 which is not four digit. So, this is not the case.<br /><br />If n ends in 6, n-1 ends in 5 i.e., n = 16k and n = 625m+1. The least possible value of m is 15 which makes n 9376.Anonymoushttps://www.blogger.com/profile/05482063307493931410noreply@blogger.comtag:blogger.com,1999:blog-5871184605628305545.post-61237442517087159602012-08-13T14:33:37.717-07:002012-08-13T14:33:37.717-07:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/05482063307493931410noreply@blogger.comtag:blogger.com,1999:blog-5871184605628305545.post-52262146563497391302012-08-09T08:55:28.230-07:002012-08-09T08:55:28.230-07:0093769376Anonymoushttps://www.blogger.com/profile/05482063307493931410noreply@blogger.com