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>? | ||
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| + | == Solution == | ||
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| + | Typing this now: 09:40 4/22/10 (in my english class) | ||
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| + | == Resources == | ||
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| + | {{USAMO box|year=1992|num-b=2|num-a=4}} | ||
| + | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=356413#p356413 Discussion on AoPS/MathLinks] | ||
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| + | [[Category:Olympiad Algebra Problems]] | ||
Revision as of 08:45, 22 April 2010
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 
?
Solution
Typing this now: 09:40 4/22/10 (in my english class)
Resources
| 1992 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
