+407 What is the average of all positive integers that have four digits when written in base 3, but two digits when written in base 6? Write your answer in base 10.
+539 base 3 numbers with 4 digits - 1000-2222 which is 27-80
base 6 numbers with 2 digits- 10-55 which is 6-35
the range is 27-35
the average is just the middle number for odd number consecutive positives
middle is 31
So the average of the positive integers, when written in base 3 that contains 4 digits but in base 6 contain 2 digits, is 31.
+539 base 3 numbers with 4 digits - 1000-2222 which is 27-80
base 6 numbers with 2 digits- 10-55 which is 6-35
the range is 27-35
the average is just the middle number for odd number consecutive positives
middle is 31
So the average of the positive integers, when written in base 3 that contains 4 digits but in base 6 contain 2 digits, is 31.
