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        riddles >> easy >> Set Of Summed Integers
        
(Message started by: K Sengupta on Dec 17th, 2005, 10:40pm)
Title: Set Of Summed Integers
Post by K Sengupta on Dec 17th, 2005, 10:40pm
At the outset, a set of 10 positive  whole numbers  was given. Summing nine of the said numbers in ten possible ways however yielded  only nine different sums which were:

86,87,88,89,90,91,93,94,95.

Determine these 10 whole  numbers.  
Title: Re: Set Of Summed Integers
Post by towr on Dec 18th, 2005, 12:57pm
[hide] the sum of all sums of 9 numbers should be divisible by 9, as it's nine times the sum of all numbers.
Therefore the total sum has to be 100
So we get the numbers 14,13,13,12,11,10,9,8,7,6[/hide]
Title: Re: Set Of Summed Integers
Post by WombatDeath on Dec 18th, 2005, 2:04pm
I may be missing something but I can't get that solution to work - the lowest sum I can get from nine of those numbers is 89.

Trying a different approach I arrived at the conclusion that the lowest of the 10 numbers must be either 49/9 or 51/9, at which point I decided to wash the dishes instead.
Title: Re: Set Of Summed Integers
Post by WombatDeath on Dec 18th, 2005, 2:18pm
If my earlier calculations were correct there isn't actually a solution to the problem as stated.  Although, in all honesty, I wouldn't bet my own money on my calculations being correct.
Title: Re: Set Of Summed Integers
Post by towr on Dec 18th, 2005, 2:20pm
Yeah, I'm getting confused as well (I removed another one of my posts too soon as well ::))
Title: Re: Set Of Summed Integers
Post by towr on Dec 18th, 2005, 2:30pm
If we had a 92 instead of 95, there is a solution.
[hide]14,13,12,11,10,10,9,8,7,6[/hide]
Title: Re: Set Of Summed Integers
Post by Grimbal on Dec 19th, 2005, 1:01am

on 12/18/05 at 12:57:18, towr wrote:
[hide] the sum of all sums of 9 numbers should be divisible by 9, as it's nine times the sum of all numbers.
Therefore the total sum has to be 100
So we get the numbers 14,13,13,12,11,10,9,8,7,6[/hide]

Correct approach, but sloppy calculation! :P
[hide]I also get a total sum of 100 if the sum 87 is duplicated.
But the numbers I get are:
14, 13, 13, 12, 11, 10, 9, 7, 6, 5
[/hide]
Title: Re: Set Of Summed Integers
Post by towr on Dec 19th, 2005, 4:23am
Ah, yes, that would explain it..
<insert excuse here>


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