
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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December 23rd, 2013, 11:14 AM  #1 
Newbie Joined: Dec 2013 Posts: 5 Thanks: 0  Tricky problem I need help with
The problem is too difficult to write in text, so I just uploaded a picture of it. Basically, the task is to get the value of this expression. I know, that the value is 12 (thanks to wolframalpha ), but how is it possible to get that? I just figured out, that the value is the same if you change the expression like this: 2010*2009*20142012*2008*2013 or even like this: 10*9*1412*8*13 What's the explanation? Thanks in advance. P.S. Sorry about my english, I don't live in Britain or so, just posted this on the first forum that came across me on google. 
December 23rd, 2013, 11:37 AM  #2 
Newbie Joined: Dec 2013 Posts: 5 Thanks: 0  Re: Tricky problem I need help with
Oh, and please tell me if I have posted this in the wrong section.

December 23rd, 2013, 05:33 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,902 Thanks: 882  Re: Tricky problem I need help with
Let k = 2013/(2013*2014); so k = 1/2014 : why that silly repeating term..."tricky" teacher?! (2010 + k)(2009 + k)(2014 + k)  (2012 + k)(2008 + k)(2013 + k) = 12 
December 24th, 2013, 12:39 AM  #4  
Newbie Joined: Dec 2013 Posts: 5 Thanks: 0  Re: Tricky problem I need help with Quote:
And k = 2013/20132014, the denominator is 20132014, not 2013*2014.  
December 24th, 2013, 02:09 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,902 Thanks: 882  Re: Tricky problem I need help with 
December 24th, 2013, 03:07 AM  #6  
Newbie Joined: Dec 2013 Posts: 5 Thanks: 0  Re: Tricky problem I need help with Quote:
But thanks, You made me think in a bit different way. My solution is in the picture below.  
December 24th, 2013, 03:26 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,902 Thanks: 882  Re: Tricky problem I need help with
OR (drop the "2000"): (9 + k)(10 + k)(14 + k) = k^3 + 33k^2 + 356k + 1260 [1] (8 + k)(12 + k)(13 * k) = k^3 + 33k^2 + 356k + 1248 [2] [1]  [2] = 12 Notice that 9+10+14 = 8+12+13 Must have something to do with number theory... 
December 24th, 2013, 03:39 AM  #8  
Newbie Joined: Dec 2013 Posts: 5 Thanks: 0  Re: Tricky problem I need help with Quote:
 
January 11th, 2014, 08:35 PM  #9 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 372 Thanks: 68  Re: Tricky problem I need help with
By the distributive property the entire number phrase is equal to: (2010+2009+2014)/20132014 — (2012+2008+2013)/20132014) =6033/20132014 — 6033/20132014 =0 

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