The room is called the liars' room, AKA it's a room full of liars. The statue tells you there's an odd one out, AKA one (and only one) of them tells the truth. If green or white told the truth, then the paintings that agreed with them must also tell the truth, but since that would mean more than one person telling the truth, that can't be the case. Thus, brown is the one telling the truth.
