Partition of natural numbers by 2-element sets
Source: Iran 2nd round 2012-Day2-P4
May 1, 2012
inequalitiescombinatorics proposedcombinatorics
Problem Statement
a) Do there exist -element subsets of natural numbers such that each natural number appears in exactly one of these sets and also for each natural number , sum of the elements of equals ?b) Do there exist -element subsets of natural numbers such that each natural number appears in exactly one of these sets and also for each natural number , sum of the elements of equals ?Proposed by Morteza Saghafian