Don't jump any step

Geometry Level 3

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.


The answer is 1025.

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