What is the average of all positibe integers that have four digits when written in base \(3\), but two digits when written in base \(6\)? Write your answer in \(10\).

All numbers from 27 to 35 in base 10 are: {1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022}in base 3 {43, 44, 45, 50, 51, 52, 53, 54, 55}in base 6 And the average is 31 in base 10