+537 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).
