+0  
 
0
59
3
avatar

Seven-digit telephone numbers are not allowed to begin with 0 or 1.  I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next three digits or the last three digits. For example, I can remember 389 - 3892 and 274 - 9274.  How many seven-digit telephone numbers can I remember?

 Mar 31, 2022
 #1
avatar+117105 
+1

Seven-digit telephone numbers are not allowed to begin with 0 or 1.  I can only remember a seven-digit telephone number if the first three digits (the "prefix") are equal to the next three digits or the last three digits. For example, I can remember 389 - 3892 and 274 - 9274.  How many seven-digit telephone numbers can I remember?

 

abcabc*    or     abc*abc

a cannot be 0 or 1 so 8 choices

2*   8*10*10*   10 = 16000

 Mar 31, 2022
 #2
avatar
+1

Hey Melody,

 

Turns out your answer is incorrect. What it seems like you did was overcounted the possibilites - for example say numbers are repeated (the numbers don't have to be distinct). I'm not sure how to correct for this either, any ideas?

Guest Apr 1, 2022
edited by Guest  Apr 1, 2022
 #3
avatar+117105 
0

You are right, I did double count.   

 

the only time I can see double counting is if they are all the same. 

So they all could be 2or 3or .....9 (8 possibiities)  They have been counted twice.

 

16000-8 = 15992

 

Are you able to check if that is right?

Melody  Apr 1, 2022

6 Online Users