A set of ten two-digit numbers is given. Prove that one can always choose two disjoint subsets of this set such that the sum of their elements is the same. Please remember to hide your solution. (by using the hide tags of course.. I don't literally mean that you should hide it )
Problem
Source:
Tags:
Amir Hossein
16.08.2011 16:28
If you like these problems to be added to the resources page, please tell me where should I add them?
mszew
16.08.2011 18:17
The minimum sum of any non empty subset of ten two digit numbers is trivialy $10$ and the maximum is $99+98+\cdots+90=945$ but there are $2^{10}-1=1023$ non empty subsets therefore two of them have the same sum
tonypr
17.08.2011 01:11
@amparvardi: If possible I'd prefer it be located in a Puerto Rico section under Puerto Rico Ibero TST in the Contest Resource page.. (though Puerto Rico doesn't even show up in the Contest Resource Page )