Question

Each user has a password 6 characters long where each character is an uppercase letter, a lowercase letter, or a digit. Each password must contain at least one digit. How long will it take to check every possible character combination, if each check takes one unit of time.

Answer 1

I am assumungthere are 26 lower case, 26 upper case and 10 digits that can fill any position
number of all possible cases
= 62^6 = 5.68 x 10^10 (huge)

number <b>without</b> any digits
= 52^6 = 1.977 x 10^10 (still huge)

so the number of possible cases with at least 1 digit
= number units of time
= (5.68 x 10^10) - (1.977 x 10^10)
= 10^10( 5.68 - 1.977)
= 3.703 x 10^10 units of time

Answer 2

sorry about the typo, but I am sure you were able to make sense out of it.