Difference between revisions of "2012 USAMO Problems/Problem 6"
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*[[USAMO Problems and Solutions]] | *[[USAMO Problems and Solutions]] | ||
{{USAMO newbox|year=2012|num-b=5|aftertext=|after=Last Problem}} | {{USAMO newbox|year=2012|num-b=5|aftertext=|after=Last Problem}} | ||
[[Category:Olympiad Algebra Problems]] | [[Category:Olympiad Algebra Problems]] |
Revision as of 11:07, 17 September 2012
Problem
For integer , let
,
,
,
be real numbers satisfying
For each subset
, define
(If
is the empty set, then
.)
Prove that for any positive number , the number of sets
satisfying
is at most
. For what choices of
,
,
,
,
does equality hold?
Solution
See Also
2012 USAMO (Problems • Resources) | ||
Preceded by Problem 5 |
Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |