Suppose that n is a positive integer such that in base 7, then n can be expressed as \(\overline{ABC}_7\), and in base 11, then n can be expressed as \(\overline{CBA}_{11}\). Find the largest possible value of n in base 10.
+591 We can say that 49A+7B+C=121C+11B+A. We can expand into 48A=120C+4B or 12A=30C+B or B=12A-30C. from here, I just guessed and got 502 base 7 and 205 base 11, and 247 base 10.
