Q: ??? Given the positions of the finger holes in a (spherical) wooden bowling ball, can we embed lumps of lead to make the ball fair? How unique is this solution?

"Fair" presumably means at least that

- the centre of mass is at the centre of the sphere;
- the moment of inertia is independent of the axis we choose.

Is this sufficient? Can we do even this?

In the 2D case is condition 1 enough?

[TB, 24 Jan 2002]A: Condition 1: If we can find the vertices of a tetrahedron containing the centre of the ball, then we can move the centre of mass to the centre of the ball by embedding masses at these vertices.

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