Suppose that A, B, and C are non-zero distinct digits less than 6, and suppose we have A_6 + B_6 = C_6 and B _6 + B_6 + C_6 = AA_6. Find the three-digit number ABC. (Interpret as a base-6 number with digits A and B, not as A times B. The other expressions should be interpreted in this way as well).
