MathDB

We have placed

n>3

cards around a circle, facing downwards. In one step we may perform the following operation with three consecutive cards. Calling the one on the center

B

, the two on the ends

A

and

C

, we put card

C

in the place of

A

, then move

A

and

B

to the places originally occupied by

B

and

C

, respectively. Meanwhile, we flip the cards

A

and

B

.
Using a number of these steps, is it possible to move each card to its original place, but facing upwards?

Problem Statement