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BNC
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sum of N real numbers
« on: May 11th, 2003, 12:36am » |
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The sum of N real numbers (not necessarily unique) is 20.
The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7.
What is N?
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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LZJ
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Re: sum of N real numbers
« Reply #1 on: May 11th, 2003, 12:46am » |
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N = 10 ? Wild guess 
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harpanet
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Re: sum of N real numbers
« Reply #2 on: May 11th, 2003, 8:19am » |
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I like this one. You start off thinking (well I did, anyway  ) that there could be any number of possible answers, after all we're dealing with Real numbers. But when you start to analyse it you see how restrictive the conditions are.
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Icarus
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Re: sum of N real numbers
« Reply #4 on: May 11th, 2003, 11:36am » |
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How can you do it with N=9, towr?
Here is my analysis: The remaining numbers add up to 8. The bottom three numbers must have a least one entry >= their average of 5/3. The top three numbers must have one entry less than their average of 7/3. Thus all the remaining numbers x must satisfy 5/3 <= x <= 7/3. Let K = N-6 be the count of remaining numbers. Then K(5/3) <= 8 and K(7/3) >= 8, so 24/7 <= K <= 24/5. Since K is an integer, K = 4 and N = 10.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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towr
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Re: sum of N real numbers
« Reply #5 on: May 11th, 2003, 3:14pm » |
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on May 11th, 2003, 11:36am, Icarus wrote:| How can you do it with N=9, towr? |
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I don't think I can, come to think of it..
I made some bad errors..
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Wikipedia, Google, Mathworld, Integer sequence DB
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Bozer
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Re: sum of N real numbers
« Reply #6 on: Dec 16th, 2003, 6:46am » |
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N = 10
The whole set:
{1, 2, 2, 2, 2, 2, 2, 2, 2, 3} has 10 members
subset of the three smallest:
{1 + 2 + 2} sum to 5
subset of the three largest:
{2 + 2 + 3} sum to 7
remaining memebers of the set:
{2 + 2 + 2 + 2} sum to 8
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rmsgrey
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Re: sum of N real numbers
« Reply #7 on: Dec 16th, 2003, 8:25am » |
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Well, that's the unique integer solution...
The problem specified real numbers, so there are infinitely many possible solutions, all of which must have ten numbers (as shown by Icarus)
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koolking
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Re: sum of N real numbers
« Reply #8 on: Jun 8th, 2012, 9:05pm » |
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I want to check the answer if its 10
Let me give my thinking behind it
If we assume the nos are integers then the answer is given in earlier posts
Let us take the other case
sum of largest 3 nos are 7 so the no smallest f them is less or equal to than 7/3. similarly the largest of the smallest 3 nos is >=5/3
now the sum of rest of the nos is 8
so take the 4th smallest no which is >= 5/3 so atmax we need 4.8 times of this no to make 8
also take 4th largest no min of 3.5 nos is needed of this to make 8
all the nos are between 5/3 and 7/3 so answer is we need 4 nos to make 8 and hence making of total 10 nos
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Technologeek
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Re: sum of N real numbers
« Reply #9 on: Jul 27th, 2012, 5:20pm » |
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{1, 2, 2, 2, 2, 2, 2, 2, 2, 3} has 10 members.
You can verify by yourself: lit works.
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Fundamental theorem of calculus
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littlemisschic
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Re: sum of N real numbers
« Reply #10 on: Jul 29th, 2012, 5:35pm » |
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N=2.5?
another wild guess but it seems to fit if my calcs are correct!
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SMQ
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Re: sum of N real numbers
« Reply #11 on: Jul 30th, 2012, 5:55am » |
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on Jul 29th, 2012, 5:35pm, littlemisschic wrote:N=2.5?
another wild guess but it seems to fit if my calcs are correct! |
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Can you provide an example of a list with two-and-a-half numbers in it? 
--SMQ
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--SMQ
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peoplepower
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Re: sum of N real numbers
« Reply #12 on: Jul 30th, 2012, 6:53pm » |
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on Jul 30th, 2012, 5:55am, SMQ wrote:
Can you provide an example of a list with two-and-a-half numbers in it?
--SMQ |
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Easy, {11,11,1}
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manchester121
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Re: sum of N real numbers
« Reply #13 on: Nov 4th, 2014, 12:00am » |
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sum=(n(n+1))/2
put n valve and find sum of real no...easily...
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csendra
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Re: sum of N real numbers
« Reply #14 on: Nov 5th, 2014, 11:32pm » |
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on Dec 16th, 2003, 6:46am, Bozer wrote:N = 10
The whole set:
{1, 2, 2, 2, 2, 2, 2, 2, 2, 3} has 10 members
subset of the three smallest:
{1 + 2 + 2} sum to 5
subset of the three largest:
{2 + 2 + 3} sum to 7
remaining memebers of the set:
{2 + 2 + 2 + 2} sum to 8
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nice work and the yes right is the 10 i,m agree with it
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