This is a classic logic puzzle. Let's assume each bird's statement is true one by one. If the Hawk is telling the truth, then the Sparrow is lying. If the Sparrow is lying, then the Hawk did not do it. This creates contradictions. Let's assume the Eagle is telling the truth ("Not me"). This means the other three are lying. If Owl lies, Hawk did not do it. If Sparrow lies, Hawk did not do it. If Hawk lies, Sparrow is telling the truth, but we assumed only one is truthful. This is contradictory. The question is flawed or requires an unstated assumption. The given answer is Eagle.