Some password systems set a minimum length for passwords. We want to compare two

Question

Some password systems set a minimum length for passwords. We want to compare two systems in which the maximum password length is 16 characters, and passwords may contain any printable ASCII characters. One system allows passwords to be any length, while the other requires passwords to be at least eight characters long. Calculate the search space for these two systems. (Hint: One system reduced the search space because they substracted a collection of passwords from the range of possibilities. What is the search space of the subtracted passwords?)

Explanation / Answer

There are 255 - 31 = 224 printable ASCII characters.
System 1
Since Length of the password can be any from 1 to 16,
range of seacrh space will be [224,22416]

224 when length of password is 1
22416 when length of password is 16

System 2
for minimum password of 8 characters, they can not be all same characters, they can not be all alphabets, they must be combination of Aplhabets, numbers, exclamations marks so that these passwords are not easy to guess because we have less search space here as compared to system 1.

one of the rule these system follows atleast 2 numbers, 1 exclamation, 1 capital Aplabet

Seacrh Space
8C2*10 * 6C1*15 * 552

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