tag:blogger.com,1999:blog-2400513859305780710.post6747087742251653671..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: A Little Logic Goes a Long Way. Topic: Logic/Sets. Level: AIMEJeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2400513859305780710.post-60444397588729113622005-12-12T13:13:34.000-08:002005-12-12T13:13:34.000-08:00If x=1, then y=1,2,3,4,5,6,7,8,9,10, and sum(z) = ...If x=1, then y=1,2,3,4,5,6,7,8,9,10, and sum(z) = 55+10=65.<br>If x=2, then y=1,3,5,7,9 and sum(z)=5^2+5(2)=35.<br>If x=3, then y=1,2,4,5,7,8,10 and sum(z) = 55-3(3)+3(7) = 67<br>If x=4, then y=1,3,5,7,9 and sum(z)=5^2+5(4)=45.<br>If x=5, then y=1,2,3,4,6,7,8,9 and sum(z)=55-5(2)+5(8)=85.<br>If x=6, then y=1,5,7 and sum(z) = 13+18=31.<br>If x=7, then y=1,2,3,4,5,6,8,9,10 and sum(z) = 55-7+7(9) = 111.<br>If x=8, then y=1,3,5,7,9 and sum(z)=5^2+5(8)=65.<br>If x=9, then y=1,2,4,5,7,8 and sum(z)=27+9(6)=81.<br>If x=10, then y=1,3,7,9 and sum(z)=20+10(4)=60.<br><br>Our answer is 645.<br><br>How are you REALLY supposed to do it??? :Pchess64http://www.upal.ca/adeelnoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-45444371818957628662005-12-12T18:33:46.000-08:002005-12-12T18:33:46.000-08:00Sum of all the numbers less than n and relatively ...Sum of all the numbers less than n and relatively prime to n is n\phi{n} / 2, so you just need to find \sum_{n=1}^{10} n\phi{n}/2, which is trivial.Elemennopnoreply@blogger.com