+4609 Suppose that A , B, and C are non-zero distinct digits less than 6 , and suppose we have \({AB_6}+{C_6}={C}0_6\) and \({AB_6}+{BA_6}={CC_6}\). Find the three-digit number ABC. (Interpret \(AB_6\) 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).
