+0  
 
0
98
1
avatar+325 

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.

 Dec 30, 2020

Best Answer 

 #1
avatar+536 
+2

base 3 numbers with 4 digits - 1000-2222 which is 27-80

base 6 numbers with 2 digits- 10-55 which is 6-35

the range is 27-35

the average is just the middle number for odd number consecutive positives

middle is 31

So the average of the positive integers, when written in base 3 that contains 4 digits but in base 6 contain 2 digits, is 31.

 Dec 30, 2020
 #1
avatar+536 
+2
Best Answer

base 3 numbers with 4 digits - 1000-2222 which is 27-80

base 6 numbers with 2 digits- 10-55 which is 6-35

the range is 27-35

the average is just the middle number for odd number consecutive positives

middle is 31

So the average of the positive integers, when written in base 3 that contains 4 digits but in base 6 contain 2 digits, is 31.

MooMooooMooM Dec 30, 2020

18 Online Users

avatar