Can you arrange a finite number of green and red squares on the plane, sides parallel to the axes, such that:
- Every red square intersects $M$ green squares and no red square;
- Every green square intersects $M$ red squares and no other green square?
For $M=2$, this is easy:
For $M=3$, this is more difficult, and was solved recently by dtldarek:
For $M=5$, this is impossible, because the smallest square necessarily intersects at most 4 squares of the other color.
So, the only remaining case is $M=4$: Is this possible?