Three, given any 5 points on a plane, where no three points are collinear and no four points are concyclic. If a circle passes through three of these points, and the other two points are respectively inside and outside the circle, then it is called a "good circle".
Let the number of good circles be $n$, find all possible values of $n$.

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Three, among: 5 points, take any two points $A, B$ and draw the line through $A$, $B$. If the other three points $C, D, E$ are on the same side of line $A B$, then consider $\angle A C B, \angle A D B, \angle A E B$. Without loss of generality, if $\angle A C B < 180^{\circ}$, then circle $A D B$ is the unique good circle; if $\angle A E B + \angle A C B = 180^{\circ}$, then circles $A C B, A D B, A E B$ are all good circles. This means that through two fixed points, there is either one or three good circles.

From 5 points, a total of 10 point pairs can be formed. Through each point pair, there is at least one good circle, so there are at least 10 good circles (including repeated counts). Each good circle passes through 3 point pairs, so there are at least 4 different good circles, and $n \geqslant 1$.

Connecting each pair of points among the 5 points with a line segment, each line segment is either a chord of a good circle or a common chord of 3 good circles. If there are at least 5 good circles, then they have at least 15 chords. Since there are only 10 line segments in total and each line segment contributes 1 or 3 to the count, the sum of 10 odd numbers is even, which cannot be 15, so there must be at least 6 different good circles. This means that at least 4 line segments are chords of good circles: 4 line segments have 8 endpoints, so there must be at least two line segments sharing a common endpoint, say $A B, A C$. Thus, $A B D$ and $A C D$ are both good circles, so there are at least three good circles through $A, D$.

Assume $A B, A C, A D, A E$ with the shortest one being $A B$, then $\angle A C B, \angle A D B, \angle A E B$ are all acute angles. If $C, D, E$ are on the same side of line $A B$, then there is only one good circle through $A, B$, so $C, D, E$ must be on different sides of line $A B$. In this case, since the sum of any two angles among $\angle A C B, \angle A D B, \angle A E B$ is less than $180^{\circ}$, there can only be one good circle through $A, B$, which is a contradiction.

In summary, the number of good circles $n$ must be 4.