Suppose you have four non-coplanar points.

How many spheres can be found such that all four points lie on its surface?

6
1
3
2
0
It depends
An infinite number
4

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Call the non-coplanar points, $A, B, C$ , and $D$ .

Now let the locus of all the points that are the same distance between $A$ and $B$ be the plane $P_1$ .

Let the locus of all the points that are the same distance between $B$ and $C$ be the plane $P_2$ .

And, let the locus of all the points that are the same distance between $C$ and $D$ be the plane $P_3$ .

Now, the center of the sphere must lie on all three planes, and since the points are non-coplanar, these three planes intersect at exactly one point. Therefore, exactly $\boxed{1}$ such sphere can be found.