Some street lights are turned ON and some others OFF .
Initially they are all gray because no one knows which are switched ON and OFF as the aim of the game is just locate the lights turned ON and OFF.
The number indicates how many lights are ON around the lamp itself (except himself) .
For the lamps ON the information is always true for the lights OFF is always false.
The game has a logical strategy, and always manages to find the lights to be turned OFF, but it's pretty easy to get lost in thought.
It follows that at some point you should try to turn ON a lamp and see the "congruence" between them.

Solution:

r1c1 must be switched off, otherwise r2c2 should be ON and FALSE

r2c4 must be switched off, otherwise r1c4 should be ON and FALSE

r1c3 should be off for the same logic above

r3c1 must be switched off, otherwise one or both r2c2 and r4c2 must be turned ON and FALSE

r4c1can not be turned off because it can not have 3 ON around.

r2c1must be switched off otherwise r2c2 ON and FALSE

r1c2 must be turned off, can not ever have 3 lamps ON around

r4c3 must be turned off, or at least one of r4c2 and r3c4 should be ON

r4c4 must be switched off otherwise r3c4 should be ON and FALSE

r3c3 should be turned off otherwise at least one of r4c2 and r3c4 should be ON

The remaining lamps are ON and we have the solution