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Omni-MATH / A finite set S of points in the coordinate plane is called [i]overdetermined[/i] if |S|≥2 and there exists a nonzero polynomial P(t), with real coefficients and of degree at most …

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problem

A finite set SS of points in the coordinate plane is called [i]overdetermined[/i] if |S|≥2|S|\ge 2 and there exists a nonzero polynomial P(t)P(t), with real coefficients and of degree at most |S|−2|S|-2, satisfying P(x)=yP(x)=y for every point (x,y)∈S(x,y)\in S. For each integer n≥2n\ge 2, find the largest integer kk (in terms of nn) such that there exists a set of nn distinct points that is [i]not[/i] overdetermined, but has kk overdetermined subsets.
Plain-text mathematical notation (without MathML)
A finite set S of points in the coordinate plane is called [i]overdetermined[/i] if |S|≥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)∈S. 
 
For each integer n≥2, find the largest integer k (in terms of n) such that there exists a set of n distinct points that is [i]not[/i] overdetermined, but has k overdetermined subsets.
Original LaTeX notation
A finite set $S$ of points in the coordinate plane is called [i]overdetermined[/i] 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 [i]not[/i] overdetermined, but has $k$ overdetermined subsets.

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task_id
8cd12c30-98f0-5518-bd62-4dc08e3fba9a
task_key
test--8cd12c30-98f0-5518-bd62-4dc08e3fba9a
task_revision_id
1
config / split
/ test

Official source

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