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?
The first case that you can remeber is if the next three digits are the same. There are 7*10*10= 700 ways to have the first three digits. Since you repeat the next three number again, that means that there is only 1 more digit that can be different from the rest which has 10 different options. There are 7000 ways for the first case and the second case is the same making your answer 7000*2=14000 seven-digit phone numbers.
*Correct me if something is wrong
Hope it helps!