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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination

Page

Toolbox

Search

2020 USAMO Problems/Problem 5

Problem

Solution