Tuesday,+August+17

Math Problem #11

Tina is assigning extension numbers for a new phone system in a large office building. There are 3,750 employees and each will have their own extension number. Extensions can't begin with 9, 0, or 1. How many digits will each extension number be?

Hint: Solve a simpler problem. With one digit, Tina will only be able to use the numbers 2, 3, 4, 5, 6, 7 and 8. So there could only be 7 employees. With two digits, Tina could use 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, etc.

What if... ...Tina could use 1 to start an extension number? or both 1 and 9? ...Tina had a company with a different number of employees? ...What is the largest number of employees for which two-digit extensions would be sufficient? three-digit? four-digit? etc.