## Two subset with equal sum

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Moon
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### Two subset with equal sum

Given any set of \$10\$ natural numbers between \$1\$ and \$99\$ inclusive, prove that there are two disjoint nonempty subsets of the set with equal sums of their elements.
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Navedimtiaz
Posts: 3
Joined: Thu Dec 16, 2010 2:06 pm

### Re: Two subset with equal sum

The highest sum of a subset here is 945(=90+91+92+93+94+95+96+97+98+99)
So the sum ranges from 1 to 945.
the number of subset is 1023(=2^10-1)
1023 subsets,945 sums,pigeonhole,..........................thats it \m/

Navedimtiaz
Posts: 3
Joined: Thu Dec 16, 2010 2:06 pm

### Re: Two subset with equal sum

forgot to write......Two set with same sum can have common elements.If they do,substract the sum of common elements from both sets and there will be two disjoint sets with same sum.If they don't,then the case is solved:):)