Recall, if we have a $d$-degree polynomial $f$, evaluate it at $\textbf{x}=(x_1,\ldots,x_n)$ we would get $\textbf{y}=(y_1,\ldots,y_n)$, where $f(x_i)=y_i$ and $d+1 \leq n$. The reverse is also true, so given $n$ pairs of $(x_i,y_i)$ we can interpolated polynomial $f$ whose degree is $d$.
Question: Is there any $n$ pairs $(x_i, y_j)$, where $i \neq j, y_i \in \textbf{y}, x_i \in \textbf{x},$ whose interpolation results in a polynomial, $f'$, where $\deg(f')\leq d$ ?
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