You participate in a quiz show in which you are shown two locked boxes, one of which contains a cookie and the other a gold bar. The keys to the boxes are held by two ladies, one of whom always tells lies and the other always tells the truth. You don not know which is which. You are allowed one question to be put to one of the ladies. How can you discover which box contains the gold bar? (What assumptions do you need to make?)

Just ask any one of them "Is the one telling lies with the box containing gold bar?"

If the answer is 'yes', go for the other box, otherwise, this is the box you want.

... make use of a paradox. You can derive answers to similar problems by constructing a paradox of appropriate reference.

Thanks.