The famous Portia's casket problem Gold casket: the portrait isn't in the silver casket. Silver: the portrait isn't in this casket. Lead: the portrait is in this casket. At least one of the statements was true and at least one of them was false. Which casket contains the portrait. If you say any one of the three statements is true, you will end up with all of them being true.

If it is in lead, all the statements are true. If it is in silver, they are all false. If it is in gold, gold and silver are true, lead is false. Only gold is acceptable