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 either 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?


I know this question was answered earlier, but the answer was incorrect. I attempted to solve this by using PIE and completementary counting, but I got stuck.

 Apr 7, 2020

You might want to explain how you used PIE and complimentary counting for this problem because it should be a casework problem.

 Apr 7, 2020

there are 8*10^6 = 8,000,000 total phone numbers

 Apr 7, 2020

I'm not a 100 percent sure on this one, so you may wanna check my work before.  


Let's first start with the most restrictive restriction:

- There has to be a repeating pattern of 3 digits that is going to be repeated either by the second loop or the third loop, and stay in the first loop. 


The repeating pattern has 1600 possibilities because there are 8 possibilities for the hundreds digit (2-9), and 10 possibilities for the ones and tens digit (0-10). 


8 * 10 * 10 = 800


We have to multiply by 2, because the repeating pattern can either be in the second loop of 3 digits or the 2nd one. 


Therefore 800*2 = 1600 phone numbers

 Apr 8, 2020

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