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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.

 Apr 9, 2021
 #1
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Base 3 largest 4 digit number   2222  =  8010

  smallest   base 3 number        1000 =  2710

 

Largest 2-digit base 6      55  =  3510

  smallest                          10  = 610

 

So  the numbers that are 4 digit in base 3   and 2 digit in base 6 go from 2710  thru  3510        I'll let you finsish from here......cheeky

 Apr 9, 2021

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