The Kochen-Specker Theorem says, if I understand it correctly, that the results of spin measurements cannot be predetermined independent of measurement. They get to this conclusion by describing 33 possible measurements whose results cannot all be satisfied simultaneously.
In the Free Will Theorem, this is developed further by taking two entangled particles sufficiently far away and measuring in 2 of these 33 directions. The proof seems to assume consistency of these results, so my question is this: If we had an entangled group of 33 particles rather than just 2, what would happen if all 33 directions were measured by space-like separated experimenters? The Kochen-Specker Theorem says that results can't all be consistent with one another.
I have very little background in physics so I apologize in advance if I'm misunderstanding something fundamental. I would also request that answers assume little knowledge of physics beyond what I've displayed above, though knowledge of mathematics can be assumed.