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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 5? Write your answer in base 10.

 Jun 2, 2021
 #1
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largesr base 5     44 5 = 24 in base 10

    smallest base 5    01    = 1                 Does Q allow leading zeroes?  I assumed it did

 

  sum of first 24 numbers =  24/2 (1+24)

 

24/2(1+24) /24=12.5 avg

 

 

 

 

 

 

If no leading zeroes are allowed in the base 5 numbers     then    10 - 445       is      5 - 24 in base 10

 

290/ 20 = 14.5 avg

 Jun 2, 2021

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