Question

Mark can remember only the first 4 digits of his friends phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If mark were to dial all of the possible numbers and if it takes him 21 seconds to try each one, how long it take to try every possibility

Answer 1

To start, let's find how many possibilities there are. If we have a 7 digit phone number, and we know 4 digits, then that means we have 3 left to determine. Two of the digits have 10 possibilities (0-9), while the last digit only has 9 possibilities (1-9) since we know that it isn't a 0. So 10*10*9=900. With 900 possibilities, and 21 seconds per possibility, we get 900*21=18900 seconds, or 315 minutes.