TUYMAADA 2009 S5

A magician asked a spectator to think of a three-digit number $\overline{abc}$ and then to tell him the sum of numbers $\overline{acb}$ , $\overline{bac}$ , $\overline{bca}$ , $\overline{cab}$ , and $\overline{cba}$ . He claims that when he knows this sum he can determine the original number. Is that so?