tag:blogger.com,1999:blog-15628310.post115529999137224238..comments2024-02-11T22:40:20.959-05:00Comments on Question of the day: This is trickyAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-15628310.post-1155559478265102652006-08-14T08:44:00.000-04:002006-08-14T08:44:00.000-04:00Abe explained it better than I ever could have.Abe explained it better than I ever could have.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1155521232293187392006-08-13T22:07:00.000-04:002006-08-13T22:07:00.000-04:00Part of my summer reading was Mario Livio's "The G...Part of my summer reading was Mario Livio's "The Golden Ratio." He has a nice little riff on this oddity in Chapter 5, page 104 in the 2002 paperback edition. It's good book, and worth a look if you haven't seen it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1155398416014822382006-08-12T12:00:00.000-04:002006-08-12T12:00:00.000-04:00The trick is to multiply the seventh number by 11....The trick is to multiply the seventh number by 11.<BR/><BR/>The sequence is a sort of fibonacci sequence: each number is the sum of the two previous (not the classic version starting with 1,1,2,3,5,8...). If you represent such a sequence algebraically with, say, the first two numbers as "a" and "b", forming each subsequent member by adding up the two previous, you get this:<BR/><BR/>a<BR/>b<BR/>a+b<BR/>a+2b<BR/>2a+3b<BR/>3a+5b<BR/>5a+8b<BR/>8a+13b<BR/>13a+21b<BR/>21a+34b<BR/><BR/>If you add up all of these, you get 55a+88b, which is obviously the seventh number (5a+8b) times 11. So, in any fibonacci-like sequence consisting of ten numbers, the sum can always be found by multiplying the seventh number times 11, which, in this case, is 126*11=1386.Abehttps://www.blogger.com/profile/04424868492071587450noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-1155321008013644942006-08-11T14:30:00.000-04:002006-08-11T14:30:00.000-04:001386 - it was easier to add the numbers in my head...1386 - it was easier to add the numbers in my head than try to figure out a trick to this.Mr. Donhttps://www.blogger.com/profile/04844019232053683131noreply@blogger.com