If \(a, b,\) and \(c\) are non-zero distinct digits in base 6 such that \(\overline{ABC}_6 + \overline{BCA}_6+ \overline{CAB}_6 = \overline{AAA0}_6\), find in base 6.
B = 1 and C = 3, so B + C = 4.
A==2, B==3, C==1
231 + 312 + 123 ==1110 in base 6
