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.

Guest Apr 7, 2020

#1**-1 **

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

HELPMEEEEEEEEEEEEE Apr 7, 2020

#3**+1 **

**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**

KingHTML Apr 8, 2020