Problem $1$:

Alice forgets her password. She goes to the system administrator's office, and the admin resets her password and gives Alice the new password.

$1.$ Why does the SA reset the password instead of giving Alice her previous $($forgotten$)$ password?

$2.$ Why should Alice re$-$reset her password immediately after the SA has reset it$?$

$3.$ Suppose after the SA resets Alice's password, she remembers her previous password. Alice likes her old password, so she reset it to its previous password. Would it be possible for the SA to determine that Alice has chosen the same password as before? Why or why not?