tag:blogger.com,1999:blog-3653932073268881677.post4470494851980662506..comments2014-12-10T04:12:18.338-08:00Comments on My Broadband Revolution: The Jumping Frogs ProblemSilverwaverhttp://www.blogger.com/profile/03639038581217650244noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-3653932073268881677.post-17767229433583876802010-04-24T08:37:09.176-07:002010-04-24T08:37:09.176-07:00Sorry for my bad english. Thank you so much for yo...Sorry for my bad english. Thank you so much for your good post. Your post helped me in my college assignment, If you can provide me more details please email me.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-49701206713809807382010-03-22T08:39:58.615-07:002010-03-22T08:39:58.615-07:00Approvingly your article helped me truly much in m...Approvingly your article helped me truly much in my college assignment. Hats incorrect to you enter, choice look forward for more cognate articles soon as its one of my pet issue to read.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-54880431344268529492010-03-22T01:08:59.956-07:002010-03-22T01:08:59.956-07:00Genial fill someone in on and this fill someone in...Genial fill someone in on and this fill someone in on helped me alot in my college assignement. Gratefulness you for your information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-44504951266946421712010-03-17T22:41:54.941-07:002010-03-17T22:41:54.941-07:00Nice dispatch and this fill someone in on helped m...Nice dispatch and this fill someone in on helped me alot in my college assignement. Thanks you seeking your information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-50477423568882650102010-03-17T21:26:42.563-07:002010-03-17T21:26:42.563-07:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-21858357323481111292010-03-17T16:22:59.868-07:002010-03-17T16:22:59.868-07:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-25853170998284751072010-03-13T13:26:49.307-08:002010-03-13T13:26:49.307-08:00Genial dispatch and this enter helped me alot in m...Genial dispatch and this enter helped me alot in my college assignement. Thanks you as your information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-47039403144601405892010-03-04T02:03:37.440-08:002010-03-04T02:03:37.440-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-75913357964629019862010-02-26T13:15:17.853-08:002010-02-26T13:15:17.853-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-86295989368015225322010-02-15T17:27:15.154-08:002010-02-15T17:27:15.154-08:00interesting article. I would love to follow you on...interesting article. I would love to follow you on twitter.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-25754912570991284052010-02-08T01:36:09.410-08:002010-02-08T01:36:09.410-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-25846908661474438312010-02-03T13:32:47.170-08:002010-02-03T13:32:47.170-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-30373027647770007742010-01-30T05:48:02.422-08:002010-01-30T05:48:02.422-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-53792046492051874082010-01-24T11:17:08.623-08:002010-01-24T11:17:08.623-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-47033321683908475662010-01-18T21:11:19.057-08:002010-01-18T21:11:19.057-08:00Nice dispatch and this enter helped me alot in my ...Nice dispatch and this enter helped me alot in my college assignement. Thanks you for your information.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-46570248181601741642010-01-10T00:25:48.440-08:002010-01-10T00:25:48.440-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-62823929400303528202010-01-04T15:23:26.793-08:002010-01-04T15:23:26.793-08:00Thanks to Anonymous for your encouragement. I hope...Thanks to Anonymous for your encouragement. I hope to keep the blog going this year.Silverwaverhttps://www.blogger.com/profile/03639038581217650244noreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-30644488205031660312010-01-04T15:22:08.804-08:002010-01-04T15:22:08.804-08:00You have provided some elegant ways of counting th...You have provided some elegant ways of counting the number of moves in any possible solution. I believe that I have shown that there a unique solution. If this is correct then we are only really interested in the number of moves in my solution.Silverwaverhttps://www.blogger.com/profile/03639038581217650244noreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-87457599570492460092010-01-03T18:48:21.670-08:002010-01-03T18:48:21.670-08:00Your blog keeps getting better and better! Your ol...Your blog keeps getting better and better! Your older articles are not as good as newer ones you have a lot more creativity and originality now keep it up!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-84325811777576364632009-12-27T04:33:37.269-08:002009-12-27T04:33:37.269-08:00My point is that it takes you the same number of m...My point is that it takes you the same number of moves whatever you do. Each move reduces the number of mis-ordered pairs by one. As there are (n+1)^2 -1 pairs it always takes this number of moves.<br /><br />An alternative approach would be to shuffle all of the red frogs along one (n moves) then have one yellow frog hop over all of them (one move). Then shuffle all the red frogs along again and have the next yellow frog jump all of them. Keep doing this until all the yellow frogs are correctly placed (n+1)n moves in total. Finally shuffle all the red frogs along so that they are all correctly placed. That gives (n+1)^2 -1 moves in total.Stephen Morrishttps://www.blogger.com/profile/06855578776077184085noreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-74489462673816048712009-12-27T00:29:13.185-08:002009-12-27T00:29:13.185-08:00This is a nice way to count the number of moves in...This is a nice way to count the number of moves in a solution. I think that I have shown how each case can be solved but I am still not sure why this is a unique solution. If you move in any way other than the one that I have described, I don't think that you get a solution.Geoffcobrahttps://www.blogger.com/profile/15396294291945780624noreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-60470797638163357602009-12-26T06:21:24.505-08:002009-12-26T06:21:24.505-08:00At the end we want to order them as red frogs, gap...At the end we want to order them as red frogs, gap, yellow frogs.<br /><br />Consider each pair of yellow frogs, red frogs and gaps. There are n^2 pairs of yellow frog/ red frog and 2n pairs of frog/gap.<br /><br />At the start every pair is ordered incorrectly.<br /><br />Each move we correct one pair. For example if a yellow frog jumps over two red frogs then we gain one from the gap/yellow frog pair, two from the yellow/red frog pairs and lose two from the red frog/gap pairs. This is a net gain of one.<br /><br />The total number of moves is therefore (n+1)^2 -1 regardless of strategy.Stephen Morrishttps://www.blogger.com/profile/06855578776077184085noreply@blogger.comtag:blogger.com,1999:blog-3653932073268881677.post-60549823560867205092009-12-20T08:17:16.526-08:002009-12-20T08:17:16.526-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.com