Suppose that A, B , and C are non-zero distinct digits less than 6, and suppose we have AB6+BA6=CC6 and AB6+C6=C06.Find the three-digit number ABC. (Interpret AB6 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).
+6251 You can convert all this to base 10 and solve it but to me that goes against the grain of the problem.
All the following is assumed to be in base 6
AB+C = C0
B<6, C<6, so B+C=6, This produces a carry of 1 to the left so
A+1 = C
AB+BA=CC so B+A = C mod 6
B+A=A+1 mod 6
B=1
C=6-B = 5
A=C-1 = 4
ABC = 4156
