MathDB

A circle is divided into

n

sectors (

n \geq 3

). Each sector can be filled in with either

1

0

. Choose any sector

\mathcal{C}

occupied by

0

, change it into a

1

and simultaneously change the symbols

x, y

in the two sectors adjacent to

\mathcal{C}

to their complements

1-x

1-y

. We repeat this process as long as there exists a zero in some sector. In the initial configuration there is a

0

in one sector and

1

s elsewhere. For which values of

n

can we end this process?

6