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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 \(10\)

 
yasbib555  Sep 15, 2018
edited by yasbib555  Sep 15, 2018
edited by yasbib555  Sep 15, 2018
 #1
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1)  333^(5n - 2) mod 11 = 5 always, since:

(5n -2) =333, when n = 67, it follows that:

333^333 mod 11 =5

 
Guest Sep 15, 2018
 #2
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2)-

 

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

 
Guest Sep 15, 2018

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