# 10 dimensional jump

Given a set of points in space, a jump consists of taking two points in the set, $$P$$ and $$Q$$, removing $$P$$ from the set, and replacing it with the reflection of $$P$$ over $$Q$$. Find the smallest number $$n$$ such that for any set of $$n$$ lattice points in $$10$$-dimensional-space, it is possible to perform a finite number of jumps so that some two points coincide.

This problem is from the OMO.

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