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Topic: Set Of Summed Integers (Read 316 times) |
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K Sengupta
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Set Of Summed Integers
« on: Dec 17th, 2005, 10:40pm » |
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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.
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| « Last Edit: Dec 17th, 2005, 10:43pm by K Sengupta » |
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towr
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Re: Set Of Summed Integers
« Reply #1 on: Dec 18th, 2005, 12:57pm » |
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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
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| « Last Edit: Dec 18th, 2005, 12:59pm by towr » |
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WombatDeath
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Re: Set Of Summed Integers
« Reply #2 on: Dec 18th, 2005, 2:04pm » |
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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.
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WombatDeath
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Re: Set Of Summed Integers
« Reply #3 on: Dec 18th, 2005, 2:18pm » |
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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.
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towr
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Re: Set Of Summed Integers
« Reply #4 on: Dec 18th, 2005, 2:20pm » |
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Yeah, I'm getting confused as well (I removed another one of my posts too soon as well  )
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towr
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Re: Set Of Summed Integers
« Reply #5 on: Dec 18th, 2005, 2:30pm » |
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If we had a 92 instead of 95, there is a solution.
14,13,12,11,10,10,9,8,7,6
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Grimbal
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Re: Set Of Summed Integers
« Reply #6 on: Dec 19th, 2005, 1:01am » |
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on Dec 18th, 2005, 12:57pm, towr wrote: 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 |
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Correct approach, but sloppy calculation! 
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
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| « Last Edit: Dec 19th, 2005, 4:43am by Grimbal » |
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towr
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Re: Set Of Summed Integers
« Reply #7 on: Dec 19th, 2005, 4:23am » |
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Ah, yes, that would explain it..
<insert excuse here>
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