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What is the average of all positive integers that have three digits when written in base 5, but two digits when written in base 7? Write your answer in base 10.

 Dec 2, 2020
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Base 5 ==(100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143)- From 25 to 48 in base 10

 

Base 7==(34, 35, 36, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 55, 56, 60, 61, 62, 63, 64, 65, 66)-  From 25 to 48 in base 10

 

Sum[25 to 48] =876


Average =876 / 24 =36.5

 Dec 2, 2020

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