Suppose you have $6$ light bulbs$($L$1,$L$2,...,$L$6),$ where each light bulb i$=1,...,5$ is initially off. You have $4$ switches which control the lights as follows:

switch $1$ S$1$ controls L$1,$L$2$

switch $2$ S$2$ controls L$2,$L$3$ and L$4$

switch $3$ S$3$ controls L$1,$L$5,$L$6$

switch $4$ S$4$ controls LB and LC where B$=2$ and C$=3$

What are the constraints?