1992 USAMO Problems/Problem 3

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For a nonempty set $S$ of integers, let $\sigma(S)$ be the sum of the elements of $S$. Suppose that $A = \{a_1, a_2, \ldots, a_{11}\}$ is a set of positive integers with $a_1 < a_2 < \cdots < a_{11}$ and that, for each positive integer $n \le 1500$, there is a subset $S$ of $A$ for which $\sigma(S) = n$. What is the smallest possible value of $a_{10}$?

Solution

Typing this now: 09:40 4/22/10 (in my english class)

Resources

1992 USAMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5
All USAMO Problems and Solutions