+0  
 
0
89
1
avatar

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 24, 2022
 #1
avatar+124676 
+1

The base 3 integers  with 4 digits go from

3*3 + 0*3^2  + 0 * 3^1  + 0   = 30003 = 27

to

2*3^3  + 2*3^2 + 2*3 + 2 = 22223  =  80

 

The base 5 integers with two digits  go from

1*5 + 0  =  105 =  5

to

4*5  + 4 = 445  =  24  

 

There is no overlap ....so.....no average is possible

 

cool cool cool

 Jun 24, 2022

12 Online Users

avatar