In a dark room there is a rotating round table, with 4 symmetrically located indistinguishable buttons. Each button can be either on or off, however inside the room one has no way to know what is the current state. When the 4 buttons are all on, and there is nobody inside, the room is lighted.

The problem is as follows. A person is (repeatedly) allowed to enter the room, and press whichever buttons he likes (that is, he can change the states of more than one buttons). After he steps out, he is told whether he succeeded to put the light on. At the same time, a table rotates in an unknown manner. Design a deterministic strategy to put the light on starting
from an unknown starting state.