Suppose Alice used a one$-$time pad to encrypt two different messages with $Z_3$

using the same key. The resulting ciphertexts were $21001$ and $11120.$

$($a$)$ Find a pair of plaintexts that could NOT have been the original messages.

$($b$)$ Using this example, describe why the one$-$time pad is not perfectly secret if

the same key is used more than once.