help to solve

[kapil das]

hi,


Given any set of 7 positive integers, is it true that there is some subset whose sum is divisible by 7 ?

do you have any idea??

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It is far better to discharge one's prescribed duties, even though faultily, than another's  duties perfectly. Destruction in the course of performing one's own duty is better than engaging in another's duties, for to follow another's path is dangerous.
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Try not to become a man of success,but rather try to become a man of value.
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Selfless service is the rent I pay for living on this wonderful planet.

Don’t draw conclusions until you know all the facts

P Kapil Das

[Jemshid KK]

2010/3/30 kapil das <pkap...@gmail.com>

Given any set of 7 positive integers, is it true that there is some subset whose sum is divisible by 7 ?

My language will be a little vague as I haven't taken any formal course in number theory or combinatorics.

modulo 7 space has 7 points (0,1,2,3,4,5 and 6) and around a circle, like summing 6 and 1 will take as to point 0. (6 + 1 = 0).

There for any set of 7 positive integers can be mapped into modulo 7 space as number between and including 0 and 6.

Zero-sum problem description in wikipedia says
" Explicitly this says that any multiset of 2n − 1 integers has a subset of size n the sum of whose elements is a multiple of n. This result is generally known as the EGZ theorem after its discoverers."

let's take n = 7.

2n - 1 = 13.

Now take numbers 0 - 13 and these numbers are mapped between 0 and 6 in modulo 7 space. Now there exists a zero sum for certain combination for which the number of elements are less than or equal to 7.

I can try to clarify further, if you have any question.

And I am very happy if some one can try putting it in formal style.

And I am waiting if some one can find an error in the proof / explanation.

Jemshid KK
ph: 9349101566,

[kapil das]

hi

i think this problem is also related

 one can selects 55 integers, there will be some two that differ by 9,

******************
S´reyan sva-dharmo viguna  para- dharmath sv-anusthita˜t
S´v-dharme nidhana s´reyah  para dharmo bhaya˜vahah

It is far better to discharge one's prescribed duties, even though faultily, than another's  duties perfectly. Destruction in the course of performing one's own duty is better than engaging in another's duties, for to follow another's path is dangerous.
Bhagavad Gita.
Try not to become a man of success,but rather try to become a man of value.
                                                                             Albert Einstein  

Selfless service is the rent I pay for living on this wonderful planet.

Don’t draw conclusions until you know all the facts

P Kapil Das

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[Abhimanyu Mongandh Ambalath]

I don't think that is true.

Consider the number sequence 2,4,6,8.... and so on since all of the numbers are even there need not be 

but it can be true that there will be some pair whose difference is a multiple of 9

--
Abhimanyu Mongandh Ambalath
BTech Computer Science
NIT Calicut

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