Problem $3$: As a reward for saving his daughter from pirates, the King has given you the

opportunity to win a treasure hidden inside one of three trunks. The two trunks that do not hold

the treasure are empty. To win, you must select the correct trunk. The inscriptions on Trunks $1,$

$2,$ and $3$ are "The treasure is in Trunk $3,"$ "The treasure is in Trunk $1,"$ and "This trunk is

empty." Where is the treasure? Examine all possibilities.