a ring of squares

Question

A ring of N squares, the N is a multiple of 3.

"K" squares in the ring are painted of white, and the other squares are painted black. We have a SWITCH operator, that turns the color of 3 adjacent squares in the ring, (black to white / white to black).

We want to turn all the squares in the ring to white. For which values of K (relative to N) can the goal be achieved? ?

Answer 1

k=N where N is a multiple of 3.

Since we cannot guarantee that 3 adjacent squares in the ring are black when there is an initial mix of black and white squares, no other value of k will work.