2020 USAMO Problems/Problem 5

Problem

A finite set $S$ of points in the coordinate plane is called overdetermined if $|S| \ge 2$ and there exists a nonzero polynomial $P(t)$ , with real coefficients and of degree at most $|S| - 2$ , satisfying $P(x) = y$ for every point $(x, y) \in S$ .

For each integer $n \ge 2$ , find the largest integer $k$ (in terms of $n$ ) such that there exists a set of $n$ distinct points that is not overdetermined, but has $k$ overdetermined subsets.

Solution

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2020 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6
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2020 USAMO Problems/Problem 5

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