Chapter 8.1, Problem 45E

Telephone Area Codes    Several years ago, the United States began running out of telephone numbers. Telephone companies introduced new area codes as numbers were used up, and eventually almost all area codes were used up.

45. (a)    Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0 or 1. How many area codes are there with this arrangement? How many telephone numbers does the current 7-digit sequence permit per area code? (The 3-digit sequence that follows the area code cannot start with 0 or 1. Assume there are no other restrictions.)

(b)    The actual number of area codes under the previous system was 152. Explain the discrepancy between this number and your answer to part (a).

(c)    The shortage of area codes was avoided by removing the restriction on the second digit. (This resulted in problems for some older equipment, which used the second digit to determine that a long-distance call was being made.) How many area codes are available under the new system?