Difference between revisions of "1992 USAMO Problems/Problem 3"
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| − | + | For a nonempty set <math>S</math> of integers, let <math>\sigma(S)</math> be the sum of the elements of <math>S</math>. Suppose that <math>A = \{a_1, a_2, \ldots, a_{11}\}</math>is a set of positive integers with <math>a_1 < a_2 < \cdots < a_{11}</math> and that, for each positive integer <math>n \le 1500</math>, there is a subset <math>S</math> of <math>A</math> for which <math>\sigma(S) = n</math>. What is the smallest possible value of <math>a_{10}</math>? | |
Revision as of 17:38, 5 April 2009
For a nonempty set 
of integers, let 
be the sum of the elements of . Suppose that 
is a set of positive integers with 
and that, for each positive integer 
, there is a subset of 
for which 
. What is the smallest possible value of 
?
