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1st December 2017, 11:47 PM  #1 
Graduate Poster
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Math experts: What is the value of this expression?
This is from a mathematics qualification pretest from an online physics course. I'm not sure I agree with the official answer. I'm curious what you all think?
What is the value of the following expression? 
1st December 2017, 11:56 PM  #2 
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2nd December 2017, 12:01 AM  #3 
Critical Thinker
Join Date: Dec 2008
Posts: 365

Python agrees:
Code:
>>> total = 0 >>> for j in (1,2): ... for k in (2,3): ... for l in (3,4): ... total += j + k + l ... >>> total 60 
2nd December 2017, 12:07 AM  #4 
Penultimate Amazing
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So you're saying that Jabba is numerically immortal?

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2nd December 2017, 12:23 AM  #5 
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2nd December 2017, 12:25 AM  #6 
Critical Thinker
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Posts: 365

Shortest answer?
Averages of each range (12, 23, 34) are 1.5, 2.5, 3.5. Sum of those is 7.5. Eight combinations summed and 8 x 7.5 = 60. 
2nd December 2017, 12:14 PM  #7 
Philosopher
Join Date: Jun 2010
Posts: 5,930

There's three sigma symbols in the equation, and twenty symbols total. 3*20 = 60.

2nd December 2017, 04:42 PM  #8 
Critical Thinker
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Funny, but let's say we change the ranges for each sigma so that instead of 12, 23, and 34 we're summing over (say) 15, 37, and 59.
Averages for the three new ranges are 3, 5, 7 which sum to 15. And there are 5 x 5 x 5 = 125 combinations. 125 x 15 = 1875. Using averages like this works because fundamentally everything we'e doing is addition and addition is also commutative, and finally the sigma operation is spanning a uniform range of values... But there are still 20 symbols. Hmm.... waiting for your new "answer"! ;) 
2nd December 2017, 04:50 PM  #9 
Philosopher
Join Date: May 2007
Posts: 6,913

May I ask a historical question?
The symbols in that mathematical equation when would they have come into existence? Or put another way how far back in time could you go and still have an educated man understand that equation? I'm asking because I am thinking of stealing that for a book but it is set in 1839 and would that be possible to write at that time? Thanks 
2nd December 2017, 05:35 PM  #10 
Critical Thinker
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Posts: 365

According to wikipedia (https://en.wikipedia.org/wiki/Histor...tical_notation) Euler used capital sigma for summation, and Euler lived in the 18th century so it seems you would be in good company to be using that notation in 1839. Euler was born in 1707 and died in 1783.

3rd December 2017, 12:40 AM  #11 
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3rd December 2017, 12:51 AM  #12 
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3rd December 2017, 06:29 AM  #13 
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