Arnold is standing at point P in triangle ABC. He moves halfway towards vertex A. He then moves halfway towards vertex B. Finally, he moves halfway towards vertex C. After these three steps, it turns out that he is back at point P. Then \[\overrightarrow{P} = x \overrightarrow{A} + y \overrightarrow{B} + z \overrightarrow{C}\] for some real numbers x, y, and z. What is the triple (x,y,z)?
I know this question has been asked before but I dont think the answer is quite right, it feels off, no concrete evidence just feels wrong
