MathDB

There are

n

points in the space such that none

4

of them lie on a plane. You can select two points

A

and

B

and move point

A

to the midpoint of line segment

AB

. It turned out that, after several moves, the points took the same places (possibly in a different order). What is the smallest value of

n

that this could happen for some

n

points?

3