Solution to "Mystery Phone Number"
The worst case scenario is that Dave goes through every wrong phone number possible before getting the right one. Dave remembers that the digits are: 4, 3, 7, 8, 2, 6, 5. This makes seven different digits. The first digit of the phone number could be any of these seven digits. The second digit could be any of the six remaining digits. The third digit could be any of the five remaining. Following this pattern, we see that there are 7! = 5040 different phone numbers that Dave could dial. The worst case scenario is that he dials all of the bad ones first (5039), saving the right one for last. Therefore, Dave must dial all 5040 phone numbers to insure that he reaches the woman.