Difference between revisions of "2024 USAMO Problems/Problem 6"
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Revision as of 17:22, 2 June 2024
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
.
See Also
2024 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.