Recently in World of Warcraft, there is a puzzle that is very similar to the "lights out" puzzle where a player needs to flip switches to turn all the lights into a specific color (in this case yellow, green, red, white). I have seen other solution to the lights out problem using linear algebra however all these uses only 2 states (on or off).
I haven't ever ran into a system of linear equation with modular operation before and would like some help solving something like:
L_1 = ((s_1 + s_2 + ...s_n + c_1 ) mod 4) L_2 = ((s_1 + s_2 + ...s_n + c_2 ) mod 4) ... L_n = ((s_1 + s_2 + ...s_n + c_n ) mod 4)
where each L has some linear combination of s + constant mod 4