# 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>? | + | 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 18:39, 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 ?