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Title: 2007 Post by: Exploited on October 08, 2007, 11:49:08 am You must solve that problem until the end of the year, because it is related to 2007 :)
The sum of five numbers is 2007: A + B + C + D + E = 2007 The sum of three of the numbers is 1000: A + B + C = 1000 Can you proof that the multiply of the numbers can be divided to 4 without residual? (eg you can split A.B.C.D.E on 4 equal parts with no remainder)? Title: Re: 2007 Post by: motomaniacs on October 08, 2007, 02:47:27 pm damn very hard to solve....
Title: Re: 2007 Post by: Joka X on October 08, 2007, 10:43:44 pm i don't think i can solve it.......i'm bad at math....
Title: Re: 2007 Post by: error398 on October 08, 2007, 11:52:17 pm thinking..
Title: Re: 2007 Post by: 3sixthy on October 09, 2007, 12:10:49 am mmm thinkin' 2 lol
Title: Re: 2007 Post by: motomaniacs on October 10, 2007, 08:31:27 pm after take a lot of time thinking
the answer is I GAVE UP :P Title: Re: 2007 Post by: keaglez on October 11, 2007, 01:35:25 am Im not bad in math at school, but this is........too................... :(
Title: Re: 2007 Post by: Exploited on October 11, 2007, 10:21:19 am Solution:
First let we say what A, B and C cannot be - they cannot be all odd (beause the sum is even) and they cannot be two even + one odd (again for the same reason). The variants left are: all even or two odd and one even 1. If all of them are even - it is obvious that their multiplication can be divided on 4: A*B*C*D*E/4 = (A/2)*(B/2)*C*D*E => because both A and B are even - they can be divided on 2 without remainder => 1. is Prooved 2. Let we check the variant if A and B are odd and C is even. Let's see what is happening with D and E: A+B+C+D+E = 2007 => D+E = 2007-(A+B+C) => D+E = 1007, which means that one of (D,E) is odd and one is even. => from the five numbers we have one even from (A,B,C) and one even from (D,E) => we have total 3 odd and 2 even - again like one we have (A*B*C/2)*(D*E/2) =>... prooved! 1. + 2. = PROOVED :) Title: Re: 2007 Post by: Jithin on October 11, 2007, 08:31:47 pm Thanks for that answer Phil... I need to improve :)
Title: Re: 2007 Post by: huatz84 on October 21, 2007, 06:18:13 am Wow,It's so hard for me...I'm bad in math.I always got zero at school..:D
Title: Re: 2007 Post by: Exploited on October 21, 2007, 08:14:29 am zero?
Title: Re: 2007 Post by: Jithin on October 21, 2007, 08:15:46 am Title: Re: 2007 Post by: huatz84 on October 21, 2007, 09:31:02 am Zero means the lowest score like the shape of egg..:D
Title: Re: 2007 Post by: keaglez on October 22, 2007, 10:55:48 pm Ow...how can you finnished your school then? ???
Haha... Just kiddin... ;D |