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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 4? Write your answer in base 10.

 
 Nov 19, 2022
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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 4? Write your answer in base 10.

 

Base 3     3^3 base10 =1000base3 = 27 base 10  smallest

                 3^4-1 base10 = 2222base3 = 80 base10  biggest

 

Base 4     4^1 = 10 base 4 = 4 base10    smallest

                 4^2-1=33 base4 = 15 base 10   biggest

 

There is no overlap so there is no answer.    0/0 is undefined

 
 Nov 19, 2022

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