2024 USAMO Problems/Problem 6
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Let be an integer and let
. A collection
of (not necessarily distinct) subsets of
is called
-large if
for all
. Find, in terms of
and
, the largest real number
such that the inequality
holds for all positive integers
, all nonnegative real numbers
, and all
-large collections
of subsets of
.
Note: For a finite set
denotes the number of elements in
.