[ska]

In general on the plane, you can fit a polynomial of n-1 degree exactly to n distinct points (i.e. it will pass through those points)

This least to an easy way to demonstrate the evils of over-fitting :)

[connorcpu]

And there is exactly 1 polynomial of degree n-1 that will match n points ;)

[ska]

It's true! I somehow missed a "unique" there, too late to edit.