2015 USAMO Problems/Problem 6
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Problem 6
Consider 
, and let 
be a multiset of positive integers. Let 
. Assume that for every 
, the set 
contains at most 
numbers. Show that there are infinitely many for which the sum of the elements in is at most 
. (A multiset is a set-like collection of elements in which order is ignored, but repetition of elements is allowed and multiplicity of elements is significant. For example, multisets 
and 
are equivalent, but 
and differ.)
