MathDB

Let

n \ge 3

cells be arranged into a circle. Each cell can be occupied by

0

1

. The following operation is admissible: Choose any cell

C

occupied by a

1

, change it into a

0

and simultaneously reverse the entries in the two cells adjacent to

C

(so that

x,y

become

1 - x

1 - y

). Initially, there is a

1

in one cell and zeros elsewhere. For which values of

n

is it possible to obtain zeros in all cells in a finite number of admissible steps?

Problem Statement